Let me start with the fact that you have a '96 and therefore it is a little more expensive to tune. You have several options and it will do a lot of good things for your car. Unfortunately, the PCM has nothing to do with the problems that you list.
- I would go through the underhood and underdash areas, find the ground connections, and clean them. Bad grounds can cause some of the problems that you list.
- The digital dashes were known to have a problem with two resistors becoming unsoldered. Do a search (this forum, the other forum, web) and you will find some specific repair instructions.
- Your dome light stays on because the circuit is grounded somewhere. Pull out each door switch and make sure that there is a wire hooked to it. The wire may have fallen off and is grounding inside the door frame. Verifiy that your dash dimmer is not turned all the way up until it clicks. Also verify that you feel a click when you turn the dimmer all the way up.