You forgot Encode::Unicode.
I had to use Tk::JPEG and use Tk::PNG.

You forgot to use strict. It would have alerted you the lexical problems that you had. Don't forget to declare all your variables.
You also forgot to put single-quotes around your colors, like 'White'.

pp --gui -o gui.exe your_fixed_script.pl
[download]

#!/usr/bin/perl

use strict;
use warnings;
use Cwd;
use GD;
use Encode::Unicode;
use Tk;
use Tk::JPEG;
use Tk::PNG;
use Tk::Pane;
use Tk::StayOnTop;
use Tk::BrowseEntry;
use Tk::widgets qw/JPEG PNG/;

my $number_of_cpus = $ENV{NUMBER_OF_PROCESSORS};
my $cwd = getcwd;

my $operation_mode_selected = "compare sequence 1 with sequence 2";
my $window_size = 10;
my $max_mismatch = 5;
my $bold_for_perfect_match = "semi-bold (4 pixel)";
my $output_picture = 1;
my $output_text = 1;

my $picture_size = 800;
my $fixed_picture_size = 1;

my $mw = MainWindow->new;
$mw->title("Chromatic Dot Plot");
$mw->geometry("852x852");
$mw->maxsize(qw(852 1500)); 
$mw->Scrolled('Pane',-scrollbars=>'osoe',-background=>'White',-sticky=
+>'nw',-gridded=>'y')->pack(-fill=>'both',-expand=>1);
$mw->Label(-background=>'White',-height=>107,-width=>138)->pack;

$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"corn
+flower blue",-text=>"C")->place(-width=>30,-x=>25,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"dark
+ slate blue",-text=>"h")->place(-width=>30,-x=>55,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"Medi
+umSeaGreen",-text=>"r")->place(-width=>30,-x=>85,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"khak
+i",-text=>"o")->place(-width=>30,-x=>115,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"Indi
+anRed",-text=>"m")->place(-width=>30,-x=>145,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"Spri
+ngGreen4",-text=>"a")->place(-width=>30,-x=>175,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"gold
+enrod2",-text=>"t")->place(-width=>30,-x=>205,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"Medi
+umOrchid1",-text=>"i")->place(-width=>30,-x=>235,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"Stee
+lBlue2",-text=>"c")->place(-width=>30,-x=>265,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"D")->place(-width=>30,-x=>333,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"O")->place(-width=>30,-x=>367,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"T")->place(-width=>30,-x=>400,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"P")->place(-width=>30,-x=>467,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"L")->place(-width=>30,-x=>500,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"O")->place(-width=>30,-x=>533,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 14",-background=>"seas
+hell2",-text=>"T")->place(-width=>30,-x=>567,-y=>10);
$mw->Label(-background=>'White',-font=>"Courier 8",-background=>"Peach
+Puff4",-foreground=>"AntiqueWhite2",-text=>"by David Rosenkranz\nUniv
+ersity Mainz, 2011")->place(-width=>183,-height=>27,-x=>630,-y=>10);
$mw->Label(-background=>'White',-font=>"Arial 8",-background=>"floral 
+white",-text=>"CHROMATIC  DOT  PLOT  draws  dot  plots with  colors  
+encoding  similarity.\nYou  can choose to compare 2  sequences by  pa
+sting or  loading them  into\nthe boxes below or to process an abitra
+ry number of sequence files.  In the\nlatter case, each sequence will
+ be plotted  against itself. Beside a  graphical\noutput CHROMATIC DO
+T PLOT can output the plot as text matrix. The results\ncan optionall
+y be saved in a folder named /CDP_results[date+time].                
+")->place(-width=>414,-height=>150,-x=>400,-y=>60);
$mw->Label(-background=>'White',-text=>"mode of operation")->place(-x=
+>25,-y=>60);
$mw->Label(-background=>'White',-text=>"window size [nt]")->place(-x=>
+25,-y=>85);
$mw->Label(-background=>'White',-text=>"maximum mismatch [nt]")->place
+(-x=>25,-y=>110);
$mw->Label(-background=>'White',-text=>"print perfect match")->place(-
+x=>25,-y=>135);
$mw->Label(-background=>'White',-text=>"save dotplot(s) as picture")->
+place(-x=>25,-y=>160);
$mw->Label(-background=>'White',-text=>"save dotplot(s) as text matrix
+")->place(-x=>25,-y=>185);
$mw->Label(-background=>'White',-text=>"Sequence 1")->place(-x=>25,-y=
+>230);
$mw->Label(-background=>'White',-text=>"Sequence 2")->place(-x=>300,-y
+=>230);
$mw->Label(-background=>'White',-text=>"Sequence files to process")->p
+lace(-x=>615,-y=>230);
$mw->Label(-background=>"grey50")->place(-width=>1000,-height=>2,-x=>2
+,-y=>500);

my $be_operation_mode = $mw->BrowseEntry(-variable=>\$operation_mode_s
+elected,-font=>"Arial 8",-width=>32,-listwidth=>214,-listheight=>2,-s
+tate=>'readonly')->place(-x=>150,-y=>60);
$be_operation_mode->insert('end',"compare sequence 1 with sequence 2",
+"process sequence files from list");
$mw->Entry(-width=>5,-justify=>'right',-font=>"Arial 8",-textvariable=
+>\$window_size)->place(-height=>20,-x=>150,-y=>85);
$mw->Entry(-width=>5,-justify=>'right',-font=>"Arial 8",-textvariable=
+>\$max_mismatch)->place(-height=>20,-x=>150,-y=>110);
my $be_bold_for_perfect_match = $mw->BrowseEntry(-variable=>\$bold_for
+_perfect_match,-font=>"Arial 8",-width=>32,-listwidth=>214,-listheigh
+t=>3,-state=>'readonly')->place(-x=>150,-y=>135);
$be_bold_for_perfect_match->insert('end',"regular (1 pixel)","semi-bol
+d (4 pixel)","bold (9 pixel)");
$mw->Checkbutton(-background=>'White',-activebackground=>'White',-vari
+able=>\$output_picture)->place(-height=>14,-width=>26,-x=>170,-y=>165
+);
$mw->Checkbutton(-background=>'White',-activebackground=>'White',-vari
+able=>\$output_text)->place(-height=>14,-width=>26,-x=>170,-y=>190);

my $seq;
my $seq1;
my $seq2;
my $copy_text;
my $sequence_1_box = $mw->Scrolled("Text",-scrollbars=>'oe')->place(-x
+=>25,-y=>250,-width=>200,-height=>200);
my $sequence_2_box = $mw->Scrolled("Text",-scrollbars=>'oe')->place(-x
+=>300,-y=>250,-width=>200,-height=>200);
$mw->Button(-font=>"Arial 8",-text=>"clear seq.",-command=>sub{$sequen
+ce_1_box->delete("1.0",'end');})->place(-width=>70,-x=>40,-y=>460);
$mw->Button(-font=>"Arial 8",-text=>"clear seq.",-command=>sub{$sequen
+ce_2_box->delete("1.0",'end');})->place(-width=>70,-x=>315,-y=>460);
$mw->Button(-font=>"Arial 8",-text=>"load file",-command=>sub{sequence
+_from_file();$sequence_1_box->delete("1.0",'end');$sequence_1_box->in
+sert("1.0",$seq);})->place(-width=>70,-x=>130,-y=>460);
$mw->Button(-font=>"Arial 8",-text=>"load file",-command=>sub{sequence
+_from_file();$sequence_2_box->delete("1.0",'end');$sequence_2_box->in
+sert("1.0",$seq);})->place(-width=>70,-x=>405,-y=>460);
$mw->Button(-font=>"Arial 8",-text=>"use demo",-command=>sub{$sequence
+_1_box->delete("1.0",'end');$sequence_2_box->delete("1.0",'end');demo
+_seq();$sequence_1_box->insert("1.0",$seq1);$sequence_2_box->insert("
+1.0",$seq2);})->place(-width=>60,-x=>232,-y=>320);    
$mw->Button(-font=>"Arial 8",-text=>"copy seq.",-command=>sub{$sequenc
+e_2_box->delete("1.0",'end');$copy_text=$sequence_1_box->get("1.0",'e
+nd');$sequence_2_box->insert("1.0",$copy_text);})->place(-width=>60,-
+x=>232,-y=>350);
$mw->Button(-font=>"Arial 8",-text=>"rotate",-command=>sub{$seq1=$sequ
+ence_1_box->get("1.0",'end');$seq2=$sequence_2_box->get("1.0",'end');
+$sequence_1_box->delete("1.0",'end');$sequence_2_box->delete("1.0",'e
+nd');$seq1=~s/\n+$//;$seq2=~s/\n+$//;$sequence_1_box->insert("1.0",$s
+eq2);$sequence_2_box->insert("1.0",$seq1);})->place(-width=>60,-x=>23
+2,-y=>380);

my $files_box = $mw->Scrolled("Listbox",-scrollbars=>'se',-selectmode=
+>"extended")->place(-x=>615,-y=>250,-width=>200,-height=>200);
$mw->Button(-font=>"Arial 8",-text=>"browse & add",-command=>\&open_fi
+les)->place(-width=>85,-x=>625,-y=>460);
$mw->Button(-font=>"Arial 8",-text=>"remove files",-command=>\&remove_
+files)->place(-width=>85,-x=>720,-y=>460);

my $display_label = $mw->Label(-background=>"grey10")->place(-width=>8
+02,-height=>802,-x=>18,-y=>570);

my $start_button = $mw->Button(-font=>"Arial 8",-text=>"START",-comman
+d=>\&check_settings)->place(-width=>50,-x=>400,-y=>520);
my $exit_button = $mw->Button(-font=>"Arial 8",-text=>"EXIT",-command=
+>sub{exit;})->place(-width=>50,-x=>465,-y=>520);
$mw->Label(-relief=>'groove',-font=>"Arial 8",-background=>'White',-te
+xt=>"color code [ID]")->place(-width=>82,-height=>25,-x=>18,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'RoyalBlue3',-text=>"100%")->
+place(-width=>40,-height=>24,-x=>100,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'RoyalBlue1',-text=>">90%")->
+place(-width=>40,-height=>24,-x=>140,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'SteelBlue2',-text=>">80%")->
+place(-width=>40,-height=>24,-x=>180,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'DarkSeaGreen1',-text=>">70%"
+)->place(-width=>40,-height=>24,-x=>220,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'khaki2',-text=>">60%")->plac
+e(-width=>40,-height=>24,-x=>260,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'goldenrod2',-text=>">50%")->
+place(-width=>40,-height=>24,-x=>300,-y=>520);
$mw->Label(-font=>"Arial 8",-background=>'brown2',-text=>">40%")->plac
+e(-width=>40,-height=>24,-x=>340,-y=>520);

my $sequence_1_length = "";
my $sequence_2_length = "";
my $seq_info_label = $mw->Label(-font=>"Arial 7",-justify=>'left',-anc
+hor=>'w',-background=>'White',-text=>"sequence 1 (horizontal) length:
+ $sequence_1_length\nsequence 2 (vertical) length: $sequence_2_length
+")->place(-width=>200,-height=>24,-x=>530,-y=>520);

MainLoop;
[download]

I tried PAR Packer and perl2exe. In both cases I get an exe file which doesn't start, although it throughs no warnings or errors. It seems there is something in the GUI that causes the trouble.

You need to show what you tried :)

Like in PAR Packer exe file doesn't run, I encounter no problems with the code you've shared.

Actually, I did find a regression in Module::ScanDeps 1.03 if I use pp -x pm.915330.pl

but pp -c pm.915330.pl works, a.exe gets created, it runs, tk gui pops up

Man! That's it. Using the -c option. Exe file gets slightly bigger and works now. THANK YOU!

Really?

I thought I had suggested that in PAR Packer exe file doesn't run ; if that was truly all it was, you would have gotten an error message along the lines of

Unpacking file "fc257124/auto/Cwd/Cwd.dll"...
Unpacking file "ffd69863/auto/Fcntl/Fcntl.dll"...
$ENV{PAR_TEMP} = ...
Can't locate deprecate.pm in @INC (@INC contains: CODE(0x1566694) ...
CODE(0x1247a34) CODE(0x1247d34)) at if.pm line 13.
BEGIN failed--compilation aborted at Switch.pm line 7.
Compilation failed in require at Tk/StayOnTop.pm line 34.
BEGIN failed--compilation aborted at Tk/StayOnTop.pm line 34.
Compilation failed in require at script/pm.915330.pl line 46.
BEGIN failed--compilation aborted at script/pm.915330.pl line 46.
[download]

You should try to pinpoint the disconnect (or my miscommunication) -- to speed things up in the future :)