You need the string equality op, 'eq', not assignment, '='. You can keep track of how many matches you have by incrementing a variable in the true branch. As it's written, the else branch is unnecessary; control goes to the next iteration anyway.

my $counter;

for (@array) {
    if ($hash{$_} eq "correct_value") {
        $counter++
        print "$_ Success\n";
        last;
    }
}

print 'We have a match.', $/ if $counter;
[download]

Update: Albannach++ quickly spotted an error, repaired.