With a change to kcott's solution, this could be achieved. Your code shows you don't understand the terniary operator something ? 'if true' : 'if false'. The 2 lines with your error are:

if($start=$i)

and

if($end=$i)

Note how I wrote the line for my $start and my $end.

my $start = $i == 0 ? $data[$i - 1][2] + 1 : 'none';
my $end = $i == $#data ? 'none' : $data[$i+1][1]-1;
[download]

You could rewrite your code to be:

        if ($special{$data[$i][0]}) 
        {
            if($i == 0)
            {
                $start = 'none';
            }
            else
            {
                $start = $data[$i - 1][2] - 1;
            }

            if($i == $#data)
            {
                $end = 'none';
            }
            else
            {
                $end = $data[$i + 1][1] - 1;
            }
            print join "\t" => $id, $data[$i][0], $start, $end;
        }
[download]

The solution would be:

#!/usr/bin/env perl -l

use strict;
use warnings;

my %special = (PF03797 => 1);

{
    local $/ = "//\n";

    while (<DATA>) {
        my ($id) = /^ID:(\w+)/;
        my @data;

        while (/HIT:(\w+).*?SEQ_START:(\d+).*?(\d+)/g) {
            push @data, [ $1, $2, $3 ];
        }

        @data = sort { $a->[2] <=> $b->[2] } @data;

        for my $i (0 .. $#data) {
            if ($special{$data[$i][0]}) {
                my $start = $i == 0 ? 'none' : $data[$i - 1][2] + 1;
                my $end = $i == $#data ? 'none' : $data[$i+1][1]-1;
                print join "\t" => $id, $data[$i][0], $start, $end;
            }
        }
    }
} 

__DATA__
ID:A0AWZ5
HIT:PF12951 SEQ_START:120  SEQ_END:350
HIT:PF03797 SEQ_START:822   SEQ_END:1073
HIT:PF15789 SEQ_START:1515   SEQ_END:1547
HIT:PF00267 SEQ_START:1200   SEQ_END:1350
//
[download]

The output from my code was:

A0AWZ5  PF03797 351     1199

Hope this helps.