I also had a engine where it would cough, sputter, pop and tried to start and run, but never quite got there. Eventually it turned out that the two LiFe battery packs I had were not capable of providing the meager amount of current needed to run the CDI unit. When I tried a different NMH pack the engine fired right up and ran like a champ. The two liFe packs charged up Ok and showed they had a nice voltage to them, but they had no current carrying capability. I since then used a better brand LiFe pack and the engine ran great with it.
I also ran into the situation where a NMH pack lost some capacity and had gotten weak at the flying field. In this case the engine would start right up and run OK, but as I went to full throttle the engine would suddenly quit. That was another one of those gotcha things. But fortunately I had it happen on the ground and not up in the air with the plane in a bad position for as dead stick landing.