Having a similar issue.
RC5+ lights and a backlit (and very warm) display turned on in middle of night. Have to remove battery to turn everything off. When I reinsert battery bike turns on by itself, and seems operable, until I try to turn off again. Lights stay on, displays go blank but center display stays backlit, and all goes unresponsive.
Diagnosis from Rad:
It appears to me that the Rad UI Display and Remote UI should be replaced. These are the center and left display and button/display units. The problem could have occurred because moisture got into the Remote UI--or debris? Something, even a tiny particle inside of the membrane switches on the handlebar, could complete the circuit and turn the bike on. It seems possible even under normal riding conditions, but I haven't seen it to date.
They've sent me an invoice to buy a new left UI Remote unit. But they cannot be purchased because they're out of stock. So, we're not able to use the bike until this gets fixed. Bike has been garage kept, out of moisture and dirt. Odd that there's a series of these occurring based on the forum hits here.