I don't know why your car dies when you try to start it, but your car not shifting out of park sounds like the same issue I had with my 2003 Saturn L200...My car would start up fine, but the anti-theft lock system would engage, and it wouldn't let me reverse. It ended up that I had a bad BCM (body control module), which is basically the computer that controls the anti-theft system. So my car thought someone was breaking into it and locked it in park. I got it replaced (I think they are about $800...pretty expensive), and my car now works fine. This may also be the reason why your door locks don't work. Hope this helps!
Recall 03V231000
Affected Cars:
Saturn
L200
2003, 2001, 2002
LS
2000
LS1
2000
LS2
2000
L100
2001, 2002
L300
2001, 2002
Electrical & Lights, July 1, 2003
Original Recall from the NHTSA
Manufacturer's Report Date:
July 1, 2003
NHTSA CAMPAIGN ID Number:
03V231000
NHTSA Action Number:
N/A
Component:
ELECTRICAL SYSTEM:IGNITION:MODULE
Potential Number of Units Affected:
239,993
Summary:
ON CERTAIN PASSENGER VEHICLES EQUIPPED WITH 2.2L L4 (L61) ENGINES, A FAILURE OF THE IGNITION CONTROL MODULE MAY CAUSE DETERIORATION IN IDLE QUALITY, REDUCTION IN OVERALL ENGINE POWER, AND THE VEHICLE MAY BE HARD TO START. CONTINUED OPERATION OF THE VEHICLE AFTER SUCH AN IGNITION MODULE FAILURE WILL RESULT IN THE ¿SERVICE ENGINE SOON¿ LIGHT FLASHING, AND MAY LEAD TO SECONDARY FAILURES OF THE CATALYTIC CONVERTER, OXYGEN SENSOR, AND EXHAUST RESONATOR.
Consequence:
FAILURE OF THE RESONATOR WILL CAUSE INCREASED EXHAUST NOISE. PROLONGED OPERATION OF THE VEHICLE FOLLOWING A RESONATOR FAILURE MAY LEAD TO A FIRE.
Remedy:
DEALERS WILL (1) REPLACE THE IGNITION CONTROL MODULE, (2) REPLACE THE IGNITION CONTROL MODULE AND SPARK PLUGS, OR (3) REPLACE THE IGNITION CONTROL MODULE, SPARK PLUGS, AND UPDATE THE POWERTRAIN CONTROL MODULE CALIBRATION. OWNER NOTIFICATION BEGAN ON AUGUST 4, 2003. OWNERS SHOULD CONTACT SATURN AT 1-800-553-6000, PROMPT 3.
Notes:
GM RECALL NO. 03033/SATURN RECALL NO. 03-C-06.CUSTOMERS CAN ALSO CONTACT THE NATIONAL HIGHWAY TRAFFIC SAFETY ADMINISTRATION¿S AUTO SAFETY HOTLINE AT 1-888-DASH-2-DOT (1-888-327-4236).

Recall data provided by the National Highway Traffic Safety Administration
