while(<IN>) {...} will read all the lines in the file, and then stops leaving the file at the end, so you use up all of the lines when checking the first key and then on the next key there are no more lines in <IN> so the while loop does nothing.

But there's no need to loop through each key in turn, you can just test if an id exists in the hash.

while(<IN>) {
   my @cols = split(/\t/,$_);
   my $id = $col[0];
   if ($GeneIDS{$id} ) {
     say "found $id";
   }
}
[download]

BTW split usually takes a pattern as the first parameter, so passing a string might not do what you expect ;)