Alternator has nothing to do with it not firing. It will make it very hard to start, even using a fully charged battery, as a charger-charged battery is less charged than one being charged by an alt. You won't be able to run it long until the battery dies either.
How big a system? A Ford 3g 130A alt will run most systems, to probly 400w, but when we start in on the competition stuff you get into the land of dual 200A alts and mulitple batteries.
Take out a sparkplug reattach the wire and lay it against the intake, or something metal. Then at night watch for spark (easier, you could do it in daylight tho) no spark = bad coil, bad ignition box, or bad dizzy sensor (ah, durasparkII something I'm farmilliar with LOL) if the sensor is bad, a reman dizzy is $55
Screwed up brakes = death. If I had your level of auto knowlege I'd get help or have it done. Bad way to die.