$command_line = "cmp -l /media/hda3/2967test/"$data[$i]" /media/hda3/2
+967test/"$data[$j]"| wc -l";
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my $path = "/media/hda3/2967test";
$command_line = "cmp -l $path/$data[$i] $path/$data[$j] | wc -l";
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But once you fix that, then you'll have a problem with this line:

$diff_count = system $command_line;
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But depending on what you are really trying to accomplish, you might want to consider using Digest::MD5 (or the *n*x "md5sum" command): just get the md5 signature for each of the files; any two files that have the same signature (and are the same size) are very likely to have identical content.

To be really careful about finding duplicate files, you may want to build a hash of arrays, with strings made up of "$md5sig $filesize" as the hash keys, and file names having identical sizes and md5s as the array elements stored at that key. Then you can run "cmp" on just the sets of files in a given array. That will reduce the amount of work to do (and the amount of printed output to review) by a lot.

update: I forgot to mention that in the code you posted, you don't actually open the input FILE handle (or get the file name for input -- maybe you meant to use the "magic diamond" operator? Anyway, here's how it might look, using the Digest::MD5 module:

#!/usr/bin/perl

use strict;
use Digest::MD5 qw/md5_base64/;

@files = <>;  # read list of file names (from @ARGV or STDIN)
chomp @files;

my %sigs;
for my $file ( @files ) {
    local $/;  # use "slurp" input mode: whole file in 1 read
    open( I, "<", $file ) or do {
        warn "$file: $!\n";
        next;
    }
    $_ = <I>;
    close I;
    my $siz = -s $file;
    my $sig = md5_base64( $_ );
    push @{$sigs{"$sig $siz"}, $file;
}

# now check for possible duplicate files
my $path = "/media/hda3/2967test";
for my $sig ( grep { @{$sigs{$_}} > 1 } keys %sigs ) {
    my @files = @{$sigs{$sig}};
    for my $i ( 1 .. $#files ) {
        for my $j ( 0 .. $i-1 ) {
            $diff = `cmp $path/$files[$i] $path/$files[$j] | wc -l`;
            print "$files[$i] - $files[$j] are duplicates\n"
               if ( $diff =~ /^\s*0/ );
        }
    }
}
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For the first one, it looks like you've got problems with your quotes; you either need to insert the concatenation operator (.) or omit the quotes before and after $data[$i]. Perl's quoting rules have double quotes (") causing variable expansion, and single quotes (') not. Take a look at this for edification.

      1 #!/usr/bin/perl -w

You should use the strict pragma as well:

        use strict;

      3 #open file
      4 open(OUTFILE, ">/media/hda3/differences.txt") or die("Unable t
+o open file");
      5 
      6 #read file into array
      7 @data = <FILE>;  

The filehandle FILE has not been opened yet so @data will be filled wi
+th nothing;

      9 #close file

All of the comments up to now have been superfluous.

     10 close (FILE);
     11 
     12 #Used to test if data is read into array
     13 #print $data[2];                                      

How is that supposed to "test if data is read into array"?

     15 #open file to save differences
     16 open(FILE, "/media/hda3/differences.txt");

You are opening the file too late to be able read it on line 7.  You s
+hould *always* verify that the file opened correctly:

        open FILE, '<', '/media/hda3/differences.txt' or die "Cannot o
+pen '/media/hda3/differences.txt' $!";

     18 #loop to determine differences
     19 for ($i=0; $i<377; $i++)
     20   {
     21   for($j=$i+1; $j<377; $j++)
     22      {

Why 377?  Why not just use the actual size of the array:

        for my $i ( 0 .. $#data ) {
          for my $j ( $i + 1 .. $#data ) {

     23      $command_line = "cmp -l /media/hda3/2967test/" $data[$i] 
+" /media/hda3/2967test/" $data[$j] "| wc -l";

There should be operators between the strings and the variables:

             $command_line = "cmp -l /media/hda3/2967test/" . $data[ $
+i ] . " /media/hda3/2967test/" . $data[ $j ] . " | wc -l";

Or just use string interpolation:

             $command_line = "cmp -l /media/hda3/2967test/$data[$i] /m
+edia/hda3/2967test/$data[$j] | wc -l";

     24      $diff_count = system $command_line;

system does not return what you seem to think it returns.  You probabl
+y want something like:

             my $command_line = "cmp -l /media/hda3/2967test/$data[$i]
+ /media/hda3/2967test/$data[$j]";

             my $diff_count = () = `$command_line`;

     25      print OUTFILE ($data[$i], "\t", $date[$j], "\t", $diff_co
+unt, "\n");

The strict pragma would have caught your typo, there is no @date array
+ defined.

     26      }   
     27   }
     28 
     29 #close file
     30 close(FILE);
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