I'd agree with the suggestion that it is the door 'ajar' switch(es).
Also, did 'Florida Guy's questions hit home?
To supplement his questions, after turning off the car, removing the key, and then opening the driver's door:
1. Do the power windows continue to work for about 15 minutes (15 minute 'time out' is controlled seperately by the DAB -- delay accessories buss)?
2. Does the hatch release button on the door jam not work (it only works if the driver door 'ajar' switch indicates the door is open?
If the answer is yes to these two, then your driver's door 'ajar' switch (and maybe the passenger side) is bad.
By the way, these are the exact same symptoms as which occured on our 94 Coupe LT1 this year.
FYI, switches are about $20 from the dealer and for our 94 (and I [presume yours too), the switches can be replaced right through their hole, without taking the whole door apart -- see the manual.
good luck.