The latest information is that 04H and all her avionics woes is that she had a dead battery when someone tried to take her up the other day. This implies that the alternator wasn't charging the battery, which implies a main power bus undervolt (or worse). This might be due to a flaky alternator field, and golly gee, that plane has had alternator problems before.
So, I'm thinking it's a problem somewhere near the alternator and not so much with the avionics bus. This'd be good, because it'd be someone else's problem to supervise getting fixed. I opined this to the club officers yesterday, and of course no one has gotten back to me yet.