Maluenda

2007 mazda 3 2.3 automatic 113,000 miles....................
While driving on the highway, car went into limp mode. Got it home, plugged in my obd2 and found p0766. Dropped the pan, fluid was in bad shape. Replaced with all new solenoids and changed fluid with m5. Cleared codes and went for a test drive, new code pulled of p0773. It thunks into reverse, goes into 1st and second, struggles into 3rd and revs at 4th, doesnt catch. No 5th.

Dropped the pan again, fluid looked bad again, but figured it might be from staining and mixed with reserve fluid since it hasn't even gone 5 miles since the last change.
Stupid me, I changed the wrong solenoid, so I have to drop the pan a 3rd time. I will be looking at the wiring for damage, loose connectors, etc and an open circuit or short, as well as changing the e solenoid.

Can some kind, awesome person please explain to me how to check for open circuits and shorts on the solenoid harness with a multimeter? Also, what are the chances this could be the tcm? I pulled it and zip tied it for better access, that was a pain, but the pins and harness looked clean and the jelly/rubber backing was dark, but looked intact and undamaged. I know I could probably get most of my money back reselling it, but I can't afford to throw $400 parts on a guess.

Has anyone else had experience with this code?

This is my only car and as a single mom, I can't afford to go to a trannie shop. If I can't fix it, I'm SOL.

Any help appreciated, thanks for looking.