Everything points to a bad power supply. Replace it, then post your results. There was some confusion because you had a Run light, then lost it again. That made me think you could have other problems, but I don't think so now.
Go back to Steve's answers, and treat them as fact. He is the GE expert, and has never been wrong!
After you get it running, get some software and do a backup. I'm confident your program is intact for now, but you said support is long gone, so a backup will save you later if your CPU ever fails.
The major clue is the OK light. Steve said that should come on during power up. It isn't, so the power supply (or backplane) is bad.
No run light, strange handheld operation, etc. is all secondary. None of this will work right if you don't have an OK light first.
Quote from Steve:
In your case, if you can't get the OK LED with only a CPU module, your problem is quite likely the power supply.