Starting/Running Problem

[Kyle.70.C10]

Ok so i just picked up a 70 C10 last week and its having some problems starting/running...Some insight, its a 350, has new fuel pump, fuel filter, plugs, wires, cap and rotor, and edelbrock 1406 carb, and a high rise wiend intake. Ok so heres the deal, if i jump into the pickup and go to fire it up after sitting for awhile it'll pop right off and run really good, but after driving it then parking it for a few minutes to an hour i'll go back out to fire it up and it'll pop off and run then if you dont romp on it it'll die then will not start up again at all no matter how much you crank on it...not even shooting starting fluid down the carb...yesterday i probably cranked on it for 20 minutes on and off till the battery died without it firing a single time...so i left the pickup over night and came back the next afternoon and it fired right up and ran perfectly fine, but driving down the road at a steady cruise it wanted to kinda cut out and when i stopped it wanted to die, but if you give it WOT it runs like a beast....got home let it sit for about 2 hours, go back out to start it, it fires up then dies and will not start again.....this is starting to piss me off...if anyone has any idea what could be causing this i'd surely like some insight. Thanks a lot.