How to replace the Verizon FIOS Router

If you have FiOS TV, that coax cable provides network access to your set-top boxes.

Without it, they won't get channel guides, on-demand programming, or firmware updates. They should still be able to tune to channels.

Whatever modem hardware is inside the set-top box (STB) is likely insufficient for data transfer and only designed to deal with HD content from Verizon. The RJ-45 on the STB is to give it access to a modem that can do data transfer, in order to expand its feature set to include internet resources. And even if it could access the internet through the coax port, the firmware is likely so locked down (and hacking it would breach your EULA) that it just wouldn't be possible.

Here are some alternatives:

• You might try playing with directional amplified wi-fi antennas to link up two different access points at a distance.
• You could always just run an ethernet cable along the molding and ceiling. This is fairly common where people are disinclined to drill through a wall, or unable to afford that kind of project.
• Is your router the same (or in the same location) as the central FiOS box? Then you've already got a coax run from there to the TV—that might make it easier to lay an ethernet cable alongside.
• There's always good old PowerLine, similar to MoCA you mentioned. Either allows you to use either your power grid or coax cables for data, but the adapters are expensive.

Personally I would gravitate towards just hiding an ethernet cable. Maybe I'd try the directional amplified wi-fi if I was feeling adventurous. Otherwise, I'd only use PowerLine or MoCA as a last resort if all of the other options were comparatively more expensive.

(Though with PowerLine, you open up the potential for, like, scripting your coffeemaker to turn on in the morning, or triggering the lights when your bluetooth phone comes in range of your desktop...)