1995 GMC Sierra wont start/battery dumps charge

Unfortunately, the battery tests good at 12.88 volts and 880 amps, tthe battery is rated at 770 cca.

Ok, I replaced the pos battery cable and engine to chassis ground. Then I tested in the 20 volt DC range as follows.
Battery pos to neg no load= 12.77 volt
battery pos to neg in run = 12.77 volt
battery neg to engine in run = 12.77 volt
battery neg to engine in start = 0.05 volt
battery neg to solenoid in run = 12.77 volt
battery neg to solenoid in start = 12.77 volt
starter to solenoid in run =.01 volt
Funny thing, the new cables made it worse, when I tried to start it went to zero on the trucks gauge and stayed there. When I opened the door to shut off the ignition that was in run. The fuel pump started running. Then a few minutes later, I was re-testing while my wife held the key in start, I touched the neg lead of the meter to the battery neg. And the positive lead to the block. The flashers came on and acc. Started working, the volt meter in the truck was pulsing with the flasher. They went off again when I tried to start it again. I have another complete under the hood harness, I'm about ready to change it, this is making me nuts.
The engine never does crank at all, the solenoid does not even click for the most part, maybe one click out of every ten attempts. And the voltmeter in the truck always drops from 14 volt to zero.
One other thing that I never considered til now, because I'm grabbing at straws, the air bag system has been completely disabled.

This thing is making me nuts. I decided to remove circuits to determine where the fault is. I went out and tried to start the truck, it was dead no clicking, no lights, nothing. I had run a small wire from bat ground for ease of taking readings under the truck, I touched it to the alternator case and it sparked. When I got in the truck I got a hell of a shock from the door. I disconnected the pos cable at the battery, going to the under hood fuse box to take a reading. After I reconnected it the truck started, and everything seems to work ok. Except when I apply the left turn signal. When it flashes the voltmeter, shift position indicator light, the radio display pulse with it. I'm glad it's starting, but it still isn't fixed, because I don't understand what happened. The only thing I did besides what I mentioned above is retest all the previous measurements because my wife did not hold the key in the start position as I told her. Then I wiggled the connector from the column to the chassis. Any ideas about this thing? This all happened yesterday and it still started today.

It actually contnued to do that even after I aded another ground cable ( slightly larger than the positive) in addition to the two factory grounds. I just can't for the life of me fiqure out why it all works good now. Except for the flashers that I mentioned earlier ( and that may be a bulbor flasher) I really appreciate your responses, I'm still trying to figur it out, since I dont know why it all started to work again, I cant trust it.
Tony

I want to thank you for all the information and all the fast responses. I do have one last question about this truck. Is there a way to find out what harness this truck should have for keyless entry. I am refering to what I am told is the acc. Harness, the one(s) that run behind the dash. For example, the turn, dimmer, washer hrness is 6314 and the ignition harness is 6311. Thanks again, Tony