According to the wiring diagram, battery voltage is supplied to the ECM for "memory power" via a 10-amp fuse in the engine compartment relay and fuse box, labeled "B/Alarm" and provides constant power to terminal 26 of the ECM, a red/black wire. The PCM should provide a ground to the ECM Control Relay coil from ECM terminal 27 (black/red wire) which in turn provides battery power to ECM terminal 54 (red/white wire). The white/red wire to the ECM Control relay, as well as the fuel pump relay, should be hot at all times via the 20-amp fusible link B in the Engine Compartment Relay and Fuse Box.
Check these voltages with key on and with key in Run position.
For what it's worth, the red/white wire from the ECM Control Relay also provides power to the fuel injectors, the idle speed control servo, and the Mass Air Flow sensor.
Oh, another thing to try since this seems to be somewhat intermittant would be to put the car in neutral and try to start it. If that works reliably, then the transmission range switch is likely faulty.
-Rod