1987 BMW 635 What's up

Engine Mechanical problem
1987 BMW 635 6 cyl Automatic 199000 miles

My 635 sit undriven for about 3 weeks. When I went to start it the battery was died. I tryed to jump and it took several minutes until the battery took enough juice to start the beamer. Once I got the car started I let it run for a little while Iturned it off. When I tryed to start it again the battery was to died to restart the car, so I took a battery out of a different car and put it in the beamer. The car did start right up, but died within a few minutes, I thought it might have been low on gas and that was the cause. The next morning the car start right up, I drove to a gas station less then a mile from my house and got gas. When I was leaving the gas station the car died at the stop sign but start back up after it turnover a few times. When I got to the next stop light the car died again and would not restart, it turned over but wouldn't start. Later I came back and the car started right away but died again when I came to a stop sign, after sitting a few minutes it started when I tryed to give it more gas while I was driving it would pop and backfire but it did go faster and I drove the rest of the way home.
I have tryed and checked varies things and I think I have ruled somethings out like the fuel pumps, filter, I have checked for vac leaks or loose wiring.
The thing I don't understand is that the car ran fine before the battery went died after sitting for a short time. I am wondering if having the died battery or trying to jump the car did something.
I really can't figure this out, anybody got any ideas?
Thanks for your time
Michael