'77 suzuki gs400 won't start

I'm trying to get my '77 Suzuki GS400 back in running condition, and
am having a few problems getting the bike started. The bike sat for a
few weeks while I worked on the brakes of the bike, and when I tried
to start the bike it had developed a dead battery. When I jumped the
bike with a car battery, I was able to get it started, but idled
roughly. The next day I tried to start the bike, but the battery was
dead again. I replaced the battery and tried to start it, but it
would not. After I had given up, the bike fell over (almost all the
way over to the right side) and i picked it up. I gave one last kick,
and it started, ran for about 5 seconds and died. same thing happened
again. i tried to start it again and it backfired, and then backfired
again as i tried one more time. after that i was not able to start
it.

I've tried starting with starting fluid in the cylinder and sometimes
fires and sometimes does nothing. I've got a new battery, replaced
the spark plugs, had the coils checked (as good), and taken the carb
off and blown out all the jets and passages. Any other ideas to try?
Any help would be appreciated. I'm a noobie at being a motorcycle
mechanic (and trying to learn to ride at the same time).

Thanks,
Brian