clicking chatter

About a year ago I finished installing the new ring gear, drove it around the neighborhood and parked it in the garage. My '06 was in better condition. Well now that I've watched it collecting dust in the garage for two years now I've decided to get rid of it. (Does any one want a project truck)

Now that you know the history.

I went to start it this morning and of course the battery was dead as a door nail. I tried jumping it with the wife’s van. Finally it started and as soon as it did she turned the van off and my BII died.
So lets try again dear. The second time it started and ran long enough for me to disconnect the jumpers and have the wife move the van out of the garage and back to where she parks it. Then it died again.
I figured that it was just because it has been a year since I had started it and that the gas is two years old. I figured that if I was in the cab and nursing it that it would stay running. Of course the battery was to weak to start it again. I put the battery charger on it and let it set for a while.
Then with the battery charger on it I tried starting it again and I get that old familiar clickity clack grinding sound. So I clean the battery connections and swap the solenoid in the '87 with the solenoid in the '86 either solenoid works find in the '86 and I get the same clickety clack grinding with either of them in the '87. The battery takes a full charge but doesn't keep it. I’m not ready to buy a new battery if the problem is something else so what and how should I test this problem?
It needs steady juice for the computer and everything else to work right, that battery it has in it sounds worthless. From what you've said so far it just doesn't have what it takes.
New battery time, and use a multimeter on the battery terminals once it's started to see if the alternator is putting out at least 14+ volts while running. (13.8-14.6)
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