The first easiest thing I would do is when it starts changing channels, put your thumb over the remote reciever. You have to take the back off, but you don't have to go near anything dangerous. You might also have to remove a piece of wood right under the mirror. If it stops you have a spurious IR signal causing it, maybe an alarm system or something. Not common, but it wouldn't be the first time.
If it keeps doing it, unplug the remote reciever. You can do this with it running and there's maximum 12 volts on it. If it stops then it's the remote reciever. If it keeps doing it, CAREFULLY reconnect the remote reciever and then unplug the keyboard. If it stops then it's the keyboard.
If it keeps doing it it's either the micro or the little SMD caps around it.
If you isolate it to the keyboard, like another respondent wrote, just use the remote for now. You're lucky in that set I'm pretty sure you can unplug them seperately, you can't in a direct view.
JURB