The pairing is true if the difference between end of one string and start value of the other string is greater than 300.

Just turn your words into code :)

#!/usr/bin/perl
use strict;
use warnings;

my @data;
while (<DATA>) {
    push @data, [ $_, (split ' ')[2,3] ];  # [ input-line, start, end 
+]
}

my $cnt;
for my $d1 (@data) {
    for my $d2 (@data) {
        my $dist = $d1->[1] - $d2->[2];    # start of one - end of the
+ other
        if ($dist > 300) {
            print "Pair", ++$cnt, ":\n";
            print "      ", $d2->[0];
            print "      ", $d1->[0];
            print "Distance: $dist\n";
        }
    }
}

__DATA__
ACNGYNDHNG 10 1333 1343 1152
AVDVHVHNGG 10 209 219 2916
ACNGYNDHNGARRT 14 1333 1347 4608
GNDNNVNNRHNNNNVMNNVNNT 22 1589 1611 6291456
[download]

Output:

Pair1:
      AVDVHVHNGG 10 209 219 2916
      ACNGYNDHNG 10 1333 1343 1152
Distance: 1114
Pair2:
      AVDVHVHNGG 10 209 219 2916
      ACNGYNDHNGARRT 14 1333 1347 4608
Distance: 1114
Pair3:
      AVDVHVHNGG 10 209 219 2916
      GNDNNVNNRHNNNNVMNNVNNT 22 1589 1611 6291456
Distance: 1370
[download]