My car had the exact problem for about 3 months, turned out to be a couple of things, the plunger crumbled when I touched it, so I rebuilt the carby. That helped alot, then I finally looked and the fuel solonoid wasn't getting power. The fuse had a TINY crack in it, replaced it. Sure enough she started right up. Tuned it, and fixed the timing. now running like it's EFI ;) so +1 for a carb rebuild. They're really easy to do yourself. Also, check the solonoid by checking if it "clicks" like a relay when you pull and plug the power back in to it.
Cheers!