It almost sounds like it's in need of a PCM security re-learn. When the PCM needs this relearn, as I understand the car will not let the injectors fire off.
Without knowing more, I'm not sure you had to replace the starter or battery.
My friend's uncle was having to do the relearn for about 6 months (not sure why) on his Saturn. Eventually he found the cause. As goofy as this sounds, his ignition key was worn out (it fell out of the ignition cylinder I'm told). He went and had a new key cut and the observation he made with the new key was thicker then the old one. Ever since that was done, the car has given him NO problems.
Here is the Re-learn process as posted on ZZP's web site:
10. How do I perform a security relearn?
1. Disconnect battery
2. Install new computer
3. Reconnect battery
4. Put emergency brake on to disable daytime running lights (this step is required!)
5. Make sure all doors trunk and hood are closed leave driver window down and reach in threw window
6. Try to start. If it doesn't start, leave the key in the on position for 10 min on 97-03 cars and 15 min for 04 and newer cars. The security light should turn off after this amount of time.
7. Turn off ignition for 3 seconds
8. Try and start the car. It probably won't start. Repeat step 5 two more times.
9. If this doesn't work disconnect battery for 5 seconds and then try and start the car.
If that doesn’t work, try this one:
1. Disconnect battery for 10 sec.
2. Reconnect battery
3. Turn key to ON position
4. Do not try to start vehicle, just quickly click to RUN position to engage security light
5. Let vehicle sit with key ON for 35 min.
6. Attempt to crank vehicle. Once vehicle is running, the security light may still be on
7. If security light is still on, turn key to OFF position for 5 sec.
8. Turn key to ON position and security light should turn off
9. Start vehicle and enjoy new PCM
Notes: If your car starts at any time and stays running, you are done. If your car starts and dies, try step 9. If it dies after 2 seconds after you have done these steps, you either have a bad FP resistor or the security setting in your PCM is wrong and it will need an update. Security relearn procedure will not work with the valet key!