First a few comments. You really should  use strict; and make an attempt to indent your code so that it is marginally readable to those willing to help you. You'll get quicker responses and more of them.

Note that you should prompt the user for the time range (begin and end times). Either that or specify that they type in the begin time for a given interval (seconds, minutes, hours). The first method would be simpler to implement. I've simplified your problem but you should get the gist of it:

use strict;

my ($beg, $end) = qw(00:01:20 00:02:20);
print "beg: $beg   end: $end\n";

print "Matches\n--------\n";
while (<DATA>) {
  chomp;
  if (($_ ge $beg) && ($_ le $end)) {
     print "$_\n";
  }
}

__DATA__
00:01:01
01:01:01
00:01:20
00:01:21
00:02:00
00:02:21
00:02:20
00:01:19
[download]

Results:

beg: 00:01:20   end: 00:02:20
Matches
--------
00:01:20
00:01:21
00:02:00
00:02:20
[download]

HTH,

--Jim