Low end break up......

I am putting a 1987 Jimmy back on the road after it being undriven and run for about 1 year. The fuel tank was drained and cleaned. The fuel filter has been replaced. Plugs, rotor ,cap, wires all new. It starts and idles fine. When accelerating, it breaks up badly at around 1000-1200 rpm...over that it smothes out. Cjanged the distributor as I felt the timing wasn't Get no "service engine" light and no bad codes using a reader. It is a 5.7 ltr with TBI. Someone suggested that it could just be a bad dist. cap. Any ideas??? It's driving me nuts!!! TNX