Well, here's my situation. I've got similar symptoms to the ones at the very beginning of this thread;
I pulled the bike out of the barn from winter storage on Sunday, put the battery in, which had been on the tender for about 8 hours. Didn't have enough juice to start the bike, so I plugged it back in to the tender and gave it a jump, at which point it started... idled for a few minutes... shut it off, then it started up again, but the battery was going on its 5th year, so I replaced it yesterday morning anyway with a brand new Interstate.
As soon as I put the new battery in, I hit the road and blasted from Vermont to (almost) Rochester, NY. Had no problems until about 20 miles outside of Rochester, then it just shut off (at about 80mph all the way in the left lane) and wouldn't start again. I let it sit for a few minutes and then was able to bump start it and ride about 1/4 mile off the thruway. Got it back to my apartment, pulled the side covers today, and found that connector on the 3 yellow wires between the stator and the R/R totally melted, 2 of the wires actually burned through.
Soo, new stator/RR/battery, no? It's got 43k miles on it, 25k of which are mine, and to my knowledge it's still got the original R/R, and presumably the original stator.
So that's where it's at right now. Should I just go ahead and get an R/R from Rick's and have them rewind my stator? The weather was BEAUTIFUL today in Rochester, I was so bummed to not be riding to class.