It probably doesn't work right because you're using the numeric comparison operator (==) on data that is probably strings. You should have used eq instead. But that's not all that you need to fix.

The first thing that comes to mind when I look at your code is that you're not really taking advantage of true power of hashes. Instead of walking through the hash and comparing $thing to $key, you want to use $thing as the key, like this:

foreach my $thing (@array) {
    if(exists $hash{$thing}) {
       push @new_array, $hash{$thing};
    }
}
[download]

If you're not afraid of grep, try this:

my @new_array = grep { exists $hash{$_} ? $hash{$_} : 0 } @array;
[download]

But that will fail if %hash contains false values.

Update: Was using $thing in the grep when I should have used $_. Thanks to davorg.

----
I wanted to explore how Perl's closures can be manipulated, and ended up creating an object system by accident.
-- Schemer

Note: All code is untested, unless otherwise stated