jumping and backfiring

I HAVE A 86 MR2, AND AFTER I DRIVE IT FOR 35MINUTES OR SO, IT STARTS TO JUMP AND BUCK AND IF I PUSH THE GAS PEDAL TO THE FLOOR IT HAS NO EFFECT. AFTER I PARK FOR A WHILE IT GOES AWAY AND SOME TIMES IT STAYS GONE UNTIL I DRIVE IT AT 60 TO 70 MILES AN HOUR FOR 35 TO 45 MINUTES AGAIN. IT SOMETIMES BACKFIRES. I NEED HELP! I HAVE REPLACED A FEW THINGS BUT NOTHING WORKS. NEW FUEL PUMP TO GET IT RUNNING AGAIN, GOT IT FROM AUTOZONE IS THIS THE PROBLEM.