If you shut off the car, will it not crank at all again without locking/unlocking the car, or will it only crank over and not actually start?
The 96's all had DAS2, which is only supposed to disable the fuel injection system, the starter should still crank. If it won't crank, I would assume a bad ignition switch.
The signal to activate or deactivate DAS2 is either by remote locking OR any of the door or trunk switches, can be done in any combination.
If the system seems to be being set (armed) by switching off the ignition, I would wonder if you are getting a red LED on the interior mirror when shutting off the car, it should be giving the visual confirmation through the red LED when arming, or a green one when disarming. If the red and green LED's are doing something out of the ordinary (flashing back and forth or both at the same time) then there is a problem in the system. Back and forth flashing means that there is an unauthorized start attempt. I would begin by wondering if maybe one of the door switches (or trunk switch) is giving the system a "lock" command due to a bad switch.