Roamio Basic not outputting HDMI or responding to remote

I haven't had any problems with this Roamio since I got it in April, but this morning it wasn't outputting *anything* on the HDMI. I tried switching cables and HDMI inputs on the TV, no luck. So I unplugged the Roamio, and when I plugged it back in, the green light came on, but the Roamio isn't responding to the remote (as in the amber light doesn't flash when I press buttons on the remote). However, the amber light does rapidly flash three or for times every couple minutes, seemingly at random. I don't have a component cable, so I can't test the Roamio that way. I did run an optical audio cable directly from the box to my home theater system, and it doesn't seem to be putting out any audio. Any idea what could be wrong?