1980 Kawasaki KLR 250 ignition problem

Hello! I am the proud borrower of a 1980 Kawasaki KLR 250 with 1138 (no really!) miles on it. It has been sitting for the last two years in a garage. After getting my license thru an MSF course, I am tryng to decide what style of bike I prefer before buying. This was to be a learning tool. I have disassembled, cleaned and coated the gas tank, cleaned and reassembled the carb(diaphram and all- ) changed the oil, replaced the sparkplug and battery. It took a few kick to get it to turn over the first time, but it took off with a hearty bang and started running. We stood there watching it and after about 5 min of running it just stopped. As if someone had hit the kill switch. No stuttering, just sudden death. Then it hasn't started since. We walked thru what we could of the elect system, and we believe that we can isolate it to the "black box" or what I have since discovered is the igniter. We checked the coil, the switches, the wires, the reluctor(thats what the guys called it) and we can get a good spark from the plug if we bypass. We considered weak magnets in the flywheel, but dont have specs for values(they do vary - 188 to 199).
Lights, turnsignals, horn and all work- ignition switch and such seem to be in working order. So at this point, I am looking for a bone. If I pick up the part from the manufacturer, it will cost about what my friend paid for the bike. Is there another option? Anything else that I can check? Any help would be greatly appreciated.