Ok heres an update for anyone else experiencing this same problem with their GV. BETTIN AND LOSIN, among others, insisted the problem was the solenoid. B&L was kind enough to send me his for free with the mirrors I purchased from him. So when it came I changed it ouf and the problem persisted. So I contacted the guy who sold it to me. He, too, suggested the solenoid, but I told him I'd just replaced it. So he said he'd come over after work and take a look at it. (Nice guy, right?) After a brief general electrical inspection revealed no problems, he hooked it up and the starter engaged. So he disconnected the connection coming off the solenoid and tried it again. This stopped the starter from engaging. So, he said, that means the problem is on the other side. With the battery disconnected agsin, he reconnected the connector and began running his hand from the other lead off the solenoid going back toward the battery, looking for frayed wires that may be grounding the circuit. The first thing he came to was a sleeve with two connectors in it. He disconnected and inspected them, and apparently happy with their condition, reconnected them. He continued running his hand along those wires back to the battery, finding nothing amiss. He then reconnected the battery and it worked fine. We started and stopped it about 20 times before putting it back together, semi confident is was ok, for now, at least. (I had to get to work fast, I was already 1/2 hour late) Now I realize this problem is NOT fixed, just lurking. But I now have the tools on my bike to remove the seat as well as disconnect the battery. So if this happens again, I will have some idea of where to start looking for an easy fix. I hope this information helps one of you gurus, like B&L, to figure this thing out, for once and for all, because this has been extremely frustrating!