First of all, there is very likely nothing wrong with any of the Engine Computers. All of the circuits feeding it are much too well-protected to let anything external cause a failure. There is one exception related to a grounded wire feeding alternator, but I will have to refer to my notes to describe that better. If that caused an internal jumper to burn open, there's an easy way to solve that.
The engine will idle too slowly any time the battery has been disconnected. You will have to hold the accelerator pedal down 1/4" to keep it running. There's a real simple solution for that too. Drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the pedals. That initiates the relearn of "minimum throttle". From then on, the computer will know when it must be in control of idle speed.
There won't be any diagnostic fault codes in the Engine Computer since the battery was disconnected, so the place to start is by determining if the automatic shutdown, (ASD) relay is turning on. If you don't have a scanner, use a test light to back-probe the dark green/orange wire at the ignition coil, any injector, or either smaller terminal on the back of the alternator. You should see the test light turn on for one second when you turn on the ignition switch, then it will turn off. You might hear the hum of the fuel pump at the same time. What is important is if that voltage returns when the engine is rotating, (cranking or running). If it does not return during cranking, the crankshaft position sensor and the camshaft position sensor are the main suspects. You'll need a scanner to view live data to see which signal is missing.
It sounds like you have an unrelated common starter problem. If you get a single, rather loud clunk from the starter each time you turn the ignition switch to "crank", but the starter works after cycling the ignition switch back and forth repeatedly, the contacts inside the starter solenoid are burned away. Most people just replace the entire starter, but the contacts are very inexpensive to replace separately.
The flashing heater control switches indicate memory was lost due to the battery being disconnected. You'll need to put the system into calibration mode once the other repairs are completed. I'll have to locate the instructions so I tell you the correct switches to press.
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Wednesday, January 9th, 2019 AT 5:53 PM