You sound pretty frustrated dude, but relax, there is always a reason.
You have one reply to check timing, that's good, and since it starts sometimes, and not others, that may be it.
I'm supposing your spark is crisp and blue, if not, check magneto or condensor, they don't go bad often, but they can. Also it would help if I knew what year, just in case it's really old. Have you tried starting fluid into the carb? this will tell you if it's timed correctly (only if it starts of course), but may indicate a weak spark, or too much oil in the gas perhaps, dirty air cleaner? I had a bike once that had a bad pet-**** and had these symptoms, also clogged fuel lines would account for it.
Go over every inch of hose, and wiring from the plug on back. Plugs are cheap as well, also, just because you bought a new carb, doesn't mean you didn't get a bad one, I once worked on a camaro for three days just to discover the new rotor I bought wasn't any good. I got spark, but not strong enough to lite the chump up.
Good luck.