Your Comcast Motorola DCT6416 needs to be connected to a television that is powered on if there is an HDMI cable connecting your TV to the DVR/cable box.
If you are using component video connection for one TV and an HDMI output for another TV, you might have trouble if you only have the component video connection powered on. The remote will not work when the composite cable-connected TV is on and the HDMI-connected TV is off.
Also, the remote will not work properly when both televisions are power off.
Occasionally the TV will need to be powered on before the remote will work. Some users have reported a time delay of about 10 minutes before the remote works for the TV.
Other users have reported the opposite problem. The cable box (without DVR) changes channels when the TV is off, but does not work when the TV is on. This situation might be caused by the backlight in the TV display, which dilutes or 'washes out' the IR signals. Some people have reported success by placing clear or transparent Scotch tape piece over the IR sensor on the cable box to "filter" out the TV light. You might also try placing the front face of the box in forward relative to front face of the TV.