I must say, I don't get it...why use hashes when you only use the keys?
This one works, though I've taken the liberty of using arrays instead, adding use strict, declararations and so on. I tried it with two files, each containing three identical lines, and I got:

Which build (enter full path name)?
/tmp/database.txt
NO
NO
YES
YES
NO
NO
NO
YES
NO
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#!/local/bin/perl -w

use strict;
 
my $build = '';

print "Which build (enter full path name)? \n" ;

chomp($build = <STDIN>);

my @build_file = ();
my @file_list = ();

open(FILE, "</home/me/stuff/input.txt") 
        || die "Could not open input file\n";
while(my $Line = <FILE>){
        push (@file_list, $Line);
}
close FILE;

open(BUILD_FILE, '<' . $build) || die "Could not open input file\n";
while(my $Line = <BUILD_FILE>){
        push (@build_file, $Line);
}
close BUILD_FILE;
  
foreach my $bkey (sort @build_file) {
    foreach my $line(@file_list){
            if (index($line, $bkey) >= 0){
               print "YES\n";
            }
            else{
            print "NO\n";
            }
    }
}
[download]

#!s #!s, oh baby when she moves, she moves...