A rotten transom will still "feel" solid, you have to know what you're looking for to spot it. One of the tell tale signs of a rotten transom is that someone will put a copious amount of silicon around the drive in an effort to band-aid the leak.
Another way to check for a bad transom is to tie the bow to a dock and reverse a little bit and see if the flow of water increases into the bilge. Reversing will cause the transom to flex in such a way that if it's rotted, more water will pour in.
If you have transducer or trim tabs, remove screws and pray no water comes out. If you see brown ooz under motor, you will have to pull motor and rebuild transsome. That sucks! Been there! Another way to test, if you haven't already done this is to fill boat with water (bow up) and see if water comes out around gimbal housin. If so, you are screwed too! Good luck!