Man, that's really weird. I've been playing Roland my whole life and have never had that problem. Did you try switching the power cords? Any pc power cord will work, at least on the RD. I actually had mine modified since it came with such a damn short one. They call it a stage piano, but the power cord is 6 feet long? Come on! Sorry, had to get that out.
Did you ask the store you bought it from? Roland has pretty decent tech support. If not, it could be something as easy as needed a new switch.
Really don't know, though. Let me know when you find the problem.