Please Help...Electrical/Alt. Probs!

[406cid70Chevy]

Ok, my 70 chevy 3/4 ton pickup has been sitting for about 5 months. I put some new gas in it and fire it up, it started right up no problem. I let it run for awhile and then all of the sudden it just flat out dies...no stutter or nothing. I try to crank it again, but it hardly will crank, like the battery had no juice. So I checked the battery and it's got like 14 amps. Then I try to start it again and BAM! it starts no problem but then it dies again! I try to start it but it barely will crank. So I hook some jumpers up to my car battery and it cranks up and starts. When I removed the jumper cables from my car battery it dies again!!! So I tested the alternator at autozone, it was producing the voltage, but a red light came on, which meant it was defective internally or something? So I got a new FREE alternator (lifetime warranty), and hooked it up. I turned the key and the truck acted like it didn't want to crank, but it started anyway, but then died again after only being on a few minutes!!! I don't know what to think! There are two braided copper wires on each side of the firewall, which I think are ground wires? I'm not sure. The driver side wire is not hooked up, but the passenger side one is hooked up to one of the valve cover bolts. I also replaced the voltage regulator about a year ago? Any suggestions??? Sorry it's so long, I just tried to be as detailed as possible.