Thanks for the links, guys. However, it's almost as easy just to save others the steps and copy the instructions here.
from Mario's link:
Troubleshooting: Receiver Reboot Instructions
If your set top box is not responding to either your remote control or front panel button input please be advised that you will need to do the following to resolve the issue:
* Just flip the door down on the front of your set top box and press the red button. Be patient as the box may take up to one minute to respond to this reset.
* Let the system reboot until either a picture or grey screen appears on your TV.
* Then press the red button again, which will reboot your system a second time. This should resolve the issue.
DirecTV sent out an email to dealers that describes the same process slightly differently.
The twitter says this:
HDDVR customers: If your HDDVR will NOT power on, unplug the unit from the wall, wait 15sec, then replug, & repeat 1x to restore service.
That, interestingly, addresses not powering on, while the complaints I read about here, and the one customer call I got, had to do with control, not power on.