It really sounds like a fuel problem. You said that you rebuilt the carb. that 'should' have taken care of that if the problem was there.
Did you also replace the fuel line? or lines? Does it have a primer bulb to pump? if it does there is a fuel line in the tank that quite often gets eaten away by the gas.
Also look for a fuel filter IN the gas tank, at the end of the fuel line. You should be able to snag the line with a hooked wire to pull the filter out.
If you would post all of the numbers off the engine, series etc. then some of the experts could steer you better.
Let us know.
Bob........54646 Central Wisconsin's most fun guy! Handy member since 3/14/'94