IMHO, I don't think the timing is going to keep it from starting, and if it was running OK when put away, it's unlikely the timing has changed?
What makes you believe it's getting fuel?
"A couple coughs" is a pretty good description of what some of my engines have done on the start following a botched landing? Landings that had me picking grass clippings out of the cylinder? That silicone inside the boot is pretty easily damaged to the point it will let spark leak through it to the metal boot. If this occurs, many times you'll have a very visible spark with the plug removed, but under compression, things don't go quite as well. You may get that occasional cough, followed by a puff of white smoke? Very often you can hear the spark as well?
So, is there a chance the plane was dropped while you were away? A bad landing just prior to your departure? Do you have another ign. module you can swap into it?