Where to begin...
 

The power locks on my '87 don't work and I'm not sure how to diagnose the problem. Here's what's happening: If I use the key, I can lock both doors from the passenger side. Same with unlock. Using the key on the driver's side will only lock the driver's door, I have to push down the button on the passenger side to lock it. When I try to unlock from the driver's door with the key, I have to twist the key and hold it while I open the door. After I remove the key, the door locks itself. The lock button in the center console will now unlock both doors but will not lock. Any ideas where to begin?

The thing with the drivers door unlocking sounds like a dodgy electric locking actuator/motor. It could also be causing the other symptoms by "freezing" up the whole system. You can test this by disconnecting the drivers door actuator from the circuit.
this hsould allow you to unlock/lock the passenger door from the driver side and also
lock/unlock from the console.

Colorado Steve...............yes it's a very old thread but..........can you share what the result was?.....what parts were needed?
Thanks in advance.