I know those motors well and I'll lay odds that this is a spark problem. If it's starts and runs, it's got fuel. The way those motors are made, if it's getting fuel to some cylinders, it's getting fuel to all. 100 to 1 it's not on the fuel side.
Check all the simplest things first. Try new spark plugs, check all leads going to the coils, check continuity on the spark plug leads, swap out each coil one at a time with a known good one, etc. I've been down this road more times than I care to admit...
My guess is it's most likely either a bad spark plug, a bad spark plug lead, a broken or disconnected ground wire on a coil or a bad coil.
Pulse pack, possibly but the ones on that motor tend to go completely if they go at all but it is possible that they can fail partially so some cylinders get spark and others not. Most of the time they just die completely so if it's got spark, which it does in this case, it's probably not the pulse pack.