2002 Other Saturn Models Engine Cranks and Fires but won't c

Engine Performance problem
2002 Other Saturn Models 4 cyl Front Wheel Drive Automatic 164K miles

Here's the problem: The engine cranks fine and has good battery. The engine fires for a few moments enough to disengage the starter and it runs for maybe a second and then stops. If the key is held in the crank position after the engine speed drops the starter usually re-engages but it will not fire again. If the key is cycled back to OFF and cranked again the engine will fire and run for another second before it stops. I've tried this many times. It has 3/4 of a tank of fuel. Any suggestions. I assume the ECM has a Crank Mode that seems to work fine but when it gets to the Run Mode something is not working right maybe a bad relay, solenoid or something. I've disconnected the battery to try to reset any electrical components. There are no Fault Codes or Lights.

Now for the can of worms. This car was in a flood with water over the top of the steering wheel. Its my daughter's car and she only had liability insurance and doesn't have money to get a replacement. I did all the post flood checks to ensure there were no mechanical issues with water in places it shouldn't be and everthing looked good. Any suggestions or how should I approach the troubleshooting?