Disconnect the battery for 5-7 minutes and try again (sometimes the PCM Keep Alive Memory gets scrambled when battery voltage gets very low).
Check the crankshaft position sensor:
Disconnect the electrical connector and measure the voltage from each pin (harness side, key on engine off) to the negative battery terminal--it should be 1.0 to 2.0V. If not it is likely a wiring problem, though it could mean a bad PCM.
With the connector unplugged check the resistance between the two sensor terminals (key off, engine off)--it should be 250 to 1kΩ. If not the sensor is bad, however this is not a definitive test as the sensor's output could be weak enough to not register with the PCM.
The good news is
they don't cost all that much so while it is not my nature to replace parts and hope I get lucky you may want to just go ahead and replace it...