how about something like this...

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

my $current;
my %data;
my $ok;

while (<DATA>) {

        next unless ( /^checking image file/ ... /^checking files file
+/ );  

        if ( /^checking image file <(.*?)>$/ ) {    # first line match
                $current = $1; $ok = 1;             # set our file and
+ status
                next;
        }

        if ( /media does not exist/ ) {             # a bad line 
                $ok = 0;
                next;
        }

        if ( /^checking files file/ ) {             # last line match
                $data{$current} = $ok ? "ok" : "bad";
        }
}

END {
        foreach my $k (sort keys %data) {
                print "$k is $data{$k}$/";
        }
}

__DATA__

checking image file <NT-Development_1024371283_FULL>
>copy 1 frag 1 media CC0202 host netbackup2: media does not exist
>copy 1 frag 2 media CC0202 host netbackup2: media does not exist
>copy 1 frag 3 media CC0202 host netbackup2: media does not exist
>copy 1 frag 4 media CC0202 host netbackup2: media does not exist
>copy 1 frag 5 media CC0202 host netbackup2: media does not exist
checking files file <NT-Development_1024371283_FULL.f>

checking image file <NT-Development_1024371284_FULL>
>copy 1 frag 1 media CC0202 host netbackup3: ok
>copy 1 frag 2 media CC0202 host netbackup3: ok
>copy 1 frag 3 media CC0202 host netbackup3: ok
>copy 1 frag 4 media CC0202 host netbackup3: ok
>copy 1 frag 5 media CC0202 host netbackup3: ok
checking files file <NT-Development_1024371284_FULL.f>

checking image file <NT-Development_1024371285_FULL>
>copy 1 frag 1 media CC0205 host netbackup4: media does not exist
>copy 1 frag 2 media CC0205 host netbackup4: media does not exist
>copy 1 frag 3 media CC0205 host netbackup4: media does not exist
>copy 1 frag 4 media CC0205 host netbackup4: media does not exist
>copy 1 frag 5 media CC0205 host netbackup4: media does not exist
checking files file <NT-Development_1024371285_FULL.f>
[download]

$ ./test.pl
NT-Development_1024371283_FULL is bad
NT-Development_1024371284_FULL is ok
NT-Development_1024371285_FULL is bad