i have a 1992 buick park avenue with a supercharged 3.8 engine about 143000 miles with the car at idle with a/c on in about 5 to 10 minutes it acts like it not running on all six cylinders turn off the air and drive around it returns to full power any ideas???

Just purchased this car used with 185,000 miles on it. We drove it to the store and came out and it would not start. It would just crack. First I thought the gas gauge may be off we were simply out of gas. Adding gas did not help. Next I thought maybe the something electrical, I have had the altenator cause things not to spark on another car I had, but the altneator checked out to be good. Now I think is might be the fuel pump. I can hear the pump run a little bit once the key is turned on and I know it builds some pressure because after the key is turned on I am able to get fuel coming out of the fuel rail relieve valve. Don't know though if there is enough pressure to keep things going there. The fuel does squirt out about 3 to 4 inches. Don't want to spend the money on the fuel pump and invest the time to change it and then be setting in the same spot. Other things I have considered are ignition. I checked to see the if I was getting spark on all 6 cylinders. I did this with a timing light. All 6 had some spark. Not sure what to check next. Would like a way to confirm it is the fuel pump before I get into changing it. Could it be the main computer? Would the fuel filter cause something like this? Would like help to figure out what is going wrong. thanks in advance.