OK... Here's where the 02 (specifically) gets its 'lock' signals...
Driver door key cylinder
Hatch key cylinder
Driver door panel
Passenger door panel
Internally via the Fob
The way they work is they apply a ground signal to the Smart Entrance Control Unit to tell it to lock the doors. This ground comes in on either pin 11 for the key cylinders, or pin 5 for the door controls. Here's the trickey part: figuring out which one is causing the problem. You can try to get a probe on the SECU to check for ground, but here's what your dealing with:
The other option is to unplug all all the control points and see if you can keep it unlocked with the fob. If it doesn't work, you'll likely need a new SECU as it's keeping a lock signal going to all the doors. If it does work, start adding in one control at a time to see which one is causing a problem. For the driver door cylinder, the connector _should_ be on the door, behind the plastic panel. I expect the rear door to be the same, but I've never taken it apart. Let us know what you find.