[dsraven]

when it won't start, pull a plug and check to see if the plug is dry or wet, and if there is a good blue spark. if wet it is possibly the carb float overflilling the carb and flooding the engine, if dry then maybe the fuel is draining from the carb after shut down. a poor or no spark could be due to the no battery thing where the coil is not seeing a good voltage.
-if the plugs get wet all the time from a flooding carb they will cause erratic running as well, compounded by a possible poor spark. the plug porcelain absorbs the fuel and causes a ground track.
-one thing that I have done in the past is install a clear fuel filter up near the carb so I can see if the fuel is running back to the tank. if, after running and a shut down like when it won't start for you, the filter is empty then the fuel pump valves may be to blame for allowing the drain back. there is a siphon effect that can drain the float bowl. that would explain the time to crank before it starts. the spark plugs would be dry in this case. the pump has to bring fuel all the way from the lowest point, or the tank, back up the the carb so it takes a bit before the engine sees fuel and starts.
-if it is a float problem where the float inlet valve is allowing the residual system pressure to overfill the carb then the plugs will be wet after you attempt to start. a float that is set too high or an inlet valve that is leaky can be masked when the engine is running, as long as it isn't leaking too much, because the engine will just run rich but after shut down the overfull carb will drain the overage fuel down the throat of the carb into the engine. this will make the engine hard to start if attempted too soon after the last shut down because the engine is flooded. the fuel has not had enough time to drain out past the pistons or evaporate. if this is the trouble remember the fuel is also diluting the engine oil and the oil may even smell like gas. this effect can virtually blow the oil pan and valve covers off, or distort them, when the engine is cranked and the extra fuel ignites inside the engine.
-if you crank and the engine won't start so you pull a plug and it is dry, the problem could be the drain back issue mentioned earlier. you may have a fuel pump problem where the valving is allowing the fuel to go back to tank. the siphon effect can drain the float bowl so it takes a long time to fill the carb.
-if you don't have a good blue spark then you mayhave a points/condensor/coil issue etc.

hope it helps. at least a starting point.