My first guess would be sticking valves. If there are valves stuck open, there isn't going to be enough vacuum to suck in a good breath of the air/fuel mixture. Could be a timing issue as well. There are timing marks on the flywheel that can be seen through the inspection cover on the right side of the engine. Your compression could be low, but I would think it would still fire up, just without any power.

Sounds like you have spark, or there wouldn't be the little puffs of smoke, so all you need from there is fuel and air. If the spark is there, and at the right time, then one of the other two must be off. Air usually isn't too hard to get, so it seems most times to be fuel. 

I'm not sure if I am any help with all of this, but it's a start.