2001 Audi A4 ECU - Short or Faulty

A few months ago I had parked my audi so that I could continue to work on it while not driving it daily. I put my 337 on the road and had unexpected bills.

As my car sat I would try to start it and let it run about every other day. I will give some background on the car.

2001 Audi A4 v6 Manual Trans

I had a few of the common Catalytic converter codes but when I went to scan it most recently after the battery had died, it had an ECM Fault code.

P0604 Internal Control Module Random Access Memory (RAM) Error

The car began to become hard to start.

The CEL would sometimes not illuminate with the KEY ON. Understanding there was something screwy with the ECM, I unplugged it and Plugged it back in. The CEL came on and I knew there was a good sign the car would start and it did.
I had continued this habit of unplugging the ECM just to get the car to start and run for a while. The time had finally come where I couldnt get the CEL to illuminate. I sent the ECU out to be repaired and they said the Processor was fried. Upon receiving the ecu, I installed it.
Without thinking I could do harm to this ecu, because I thought the issue was isolated to the ECU, I started the car. It ran for about 5 seconds and shut off. No CEL was displayed. The car would not start. I sent the ECU back out and they fixed it again for free but next time I would have to pay.(Understandably).

There are other issues that allowed me to drive the car for a solid year.
-Coolant Temp reading intermittent
-Oil Temp Intermittent
-Fuel Guage Inoperative
-ABS Light always on

-There is no coolant migration on the CTS plug.

-The Relay 373 on the side of the ECU clicks fine (75ohms)

I have since been out testing some grounds but need more information on what to look for. I asked the same questions on JustAsk. Com but they were vague in answering. Any help would be greatly appreciated

Thank you for any info. Peace