This actually happened to me with my 2010. Bought a reconditioned radio on Ebay for $100, had exactly the same issue. Took a meter to the rocker switches, all showed right. That's about all I really know about electrical, so it went to the dealer. Made sure they knew about the Ebay radio in a box in the tour pack.

Turns out there's a built in amp in the radio that went bad, and it's pretty common, or so they tell me. Ebay radio apparently had the same issue. Cost me $600 to replace with another reconditioned from Iron Cross in South Carolina, 3yr warranty on the radio, 1yr on the labor and I was back on the road. Iron Cross gave me $150 for the Ebay radio for parts so that end worked out.

Probably not much help, but Iron Cross is someone I'd deal with again, so there's my .02