"Doesn't work" isn't very descriptive, so its hard to help.  Do the red LEDs on the remote device buttons light up?  Using a cell phone camera to look at the transmitting end of the remote can you see flashes of light when pressing butttons?

No components respond?  Why would turning off the TV make the remote worK?  

Or do you mean that the cable box doesn't respond to the remote?  If it is the latter, turn off the cable box (unplug it, wait a couple of minutes, and then repower.  If that fixes the problem, but it recurs, and cycling cable box power restores response, return the cable box to Comcast.)