You are already looping through the hash, just use rand() to pick a random element out of the hash.

my $r = int(rand(keys %db));
my $i = 0;
foreach (keys %db) {
  if($r == $i){
    print qq(<a href="$_"><img src="/images/$db{$_}"></a>);
    last;
  }
  $i++;
}
[download]

- Tom