65 170 idles ok, starts ok, pops through carb

After sitting awhile outside my 65 Valiant with a 170 finally started up and still idles like it should. About 3 or 4 months ago I installed a remanufactured carb, reman distributor, plugs, wires, cap, rotor, coil. I set the timing to 5 BTC and it's still on that same mark today. Even when I first installed all that and had it running it ran drove around my big driveway pretty smooth and had good power, didn't try to go over 25mph though. It still popped through the carb and tried to stall out when you wanted to give it full throttle. That's what it's doing still. I noticed today when it died after we snapped the throttle the battery was totally dead. No headlights, or anything. I don't know if it was running only on the battery because the Ammeter doesn't work. Is the popping through the carb, carb related or ignition? One mechanic said that's the accelerator pump and another said it's valve problems. The valves I havent adjusted becaue the engine revs smooth and idles smooth unless you give it full throttle. It idles so quiet you can barely tell it's on. What do I need to check?