AHA!
This morning I remembered that I had disconnected the line into the gas door lock when I first got the car because it was malfunctioning and it had locked on me at the gas station once. I didn't want to take any more chances until I fixed the clip.
I reconnected the line and all is good now!
I've driven the car around this morning and the doors are working just like you guys described and open and close (all four, including the one that was sticky) when I lock/unlock the driver's door with the engine off and on. Fingers crossed!
The only thing left now is figuring out why do I have to push driver's door knob/key in to engage the lock (for locking and unlocking). Any thought?
Jose