Oh, there has been MUCH of the plugging/unplugging, removing battery, putting the battery back, etc. -- in all the different ways possible. I've tried leaving the AC plugged in overnight with the battery, then without, then resetting the PMU with the battery, then without... then with the AC, then without... then with AC and battery, then just battery, then just AC... you get the idea.
I replaced the power board with one that user AichEss sent me. It was tested fully before he sent it. It's GOT to be the logic board, at this point.