If it is running on starter fluid, I'd abandon looking any farther with the coil. You're probably NOT getting gas to the carbs. I'd go looking for fuel in the lines. If you disconnect the lines from the carbs and have a friend pull it over a few times while you watch the lines - you should see fuel pulsing out of them. If not, I would head towards the fuel pump as the culprit.
BTW - if your starter fluid does not have some type of oil in it, I wouldn't advise using it too much. Make up some pre-mix (50:1) gas and pour that in the cylinders instead.
Last thought... have you checked compression? If it is low, that would make it very hard to start, even with starter fluid.
2004 Polaris Trail RMK 136
1997 Ski Doo Summit 500
2000 Arctic Cat ZL550 ESR (in NY)
2000 Arctic Cat 440 Panther (sold)
1980 Arctic Cat Jag 3000 F/C (in NY)
"If it ain't broke, take it apart and find out why!"