If there was a short to ground, it would blow a fuse. If there was a slow drain, you wouldn't notice anything unless you let the bike sit overnight.
All my bets are your battery either needs to be charged or is no good. Charge it, get it load tested.
As for the flywheel, it's a good thing you noticed it failing before it actually chucked a magnet. Do not run that motor until you replace it with a gen2 flywheel (as O.E.M. mentioned, 1994-later) that had been appropriately modified for a gen1.
As you noticed, they area bit hard to come by. I am fresh out, so look on ebay. You have to get a little creative sometimes to find one for a reasonable price. I've had good luck in the past searching for a crankshaft. Sellers sometimes don't bother removing the flywheel, and crankshafts aren't big money sellers. One I had been watching on ebay, with the flywheel still on it, just sold for 60 bucks.
1990 EX500 - 116,000 miles as of April 9th, 2017
1988 Honda XR600 - Street legal play toy
*I have a large inventory of used factory EX parts, both gen1 and gen2, feel free to PM me if you are looking for something*