88 Mustang 5.0 GT
 

I recently bought an 88 GT 5.0 and I'm having issues with what seems like the fuel system. I have replaced the fuel pump, fuel filter and pressure regulator. Here's the issue: whenever I run the car at anything more than an idle for a few minutes the car starts acting like it is getting starved of fuel and the fuel pump will start whining very loudly. I can fix it temporarily by turning the key off and then back on, but the problem returns shortly thereafter. Also, I put a new alternator and battery in it and the battery still seems to die after running it for a while. To top it off the "check engine" light never comes on even when you first turn the key on. Could this be a clue as to what's going on? I can't seem to find any info anywhere. If anyone can provide any insight into this issue I would appreciate it. It has my buddies and I pulling our hair out. Thanks a lot!