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Make sure that you have pressed the STB Button on the top of the remote on the right.
You may also need to reprogram it. Instructions can be found here:
Note that your Router has NOTHING to do with the operation of your remote control.
I know this will sound silly, but will the remote control the STB with the TV turned off? If so, the problem may very well be IR interference from the light sensor on your TV (believe it or not!). Here is a link to a thread which discusses this issue, with a possible solution: Link
Verizon FiOS TV, Internet, and phone
QIP6416, IMG 1.6.2, Build 08.58
Keller, TX 76248