The fuel that was on your hand is normal. It doesn't mean it came from the pilot circuit though. It easily could have came from the main circuit. That was just to try to force anything out of the tiny passageways that may have gotten in there.
I just realized you're from Indiana. Where abouts? If you're close to me I'd be more than willing to come out and see what I can find. I graduated top of my class in motorcycle mechanics school in Cleveland back in '07.
Actually, when you jump a lawnmower or ATV, it's because the battery is dead, yes? If it's dead, then it does
not have a full nominal voltage of 12.6VDC (2.1VDC per cell in a 6 cell battery). So yes, there is a difference in potential, which results in an almost instantaneous charging cycle of the battery to get it to match the voltage of the stronger battery.
You
can ruin lead-acid batteries like this, and possibly even charging system components like the little grey box with cooling fins on it that serves to rectify and regulate voltage coming from the stator. Just because you haven't yet, doesn't mean you won't down the road. Best advice I can offer, whether you choose to go by it or not, is to only jump it with the engine off so the trucks charging system does not backfeed through the regulator/rectifier and fry the diodes, or worse, once that happens it can back feed into the stator and wipe it out as well.
Anyways, back on track.
You are obviously getting air. You are getting fuel, but just because you see/smell fuel doesn't mean it's getting the correct amount at the right time. Spark? Well there are insulation breakdown and resistance tests you can perform on the ignition coil and other parts of the ignition system to rule them out.
If you believe you are getting weak spark, you need to remove the plug wire from the plug and the coil. The wire will unscrew from the coil. There's a little brass stud coming out of the coil that the plug wire screws onto. It's the same way on the spark plug cap end. This stud makes contact with the wires of the plug wire. If I suspect that connection to be the culprit, I will take a pair of diagonal cutter (side cutters) and snip the last 1/4" or more off the end of the plug wire that screws into the coil or cap until you see good wire strands inside the plug wire. Once good, you can screw the plug cap back on, but leave the other end unscrewed from the coil for the next test.
If you have a meter, now is the time to place it on the resistance setting (Ohms) and stick one probe in the plug cap and the other probe into the coil end of the wire. You should see quite a high resistance, somewhere in the vacinity of 10k Ohms, if my memory serves me correctly. Reason being is there is a small ceramic insulator in the spark plug boot that has a very high resistance. If you are getting an Infinite reading or "OL" on the meter, then you need to take a flat blade screwdriver and unscrew the brass plug that holds the insulator in the cap. Remove the insulator, the spring, and oftentimes there's a tiny little spacer disk in there as well. A lot of times I'll find corrosion between the insulator and the spring. The spring is steel so it's first to corrode in there. Just for the heck of it, clean everything up with sandpaper and reassemble.
The link below will give you specs to check out the ignition and stator coils. They should be the same since most Yamaha ATV ignition systems are nearly identical.
How to Check CDI on a Yamaha Warrior | eHow.com
Atleast this will give you a direction in which to go. If you don't feel comfortable with doing any of the checks, you should really take it to a reputable shop/person to work on it.