I am sorry, but I don't know what many of the terms you used mean. These are:
Please clarify what these are.
I have no "[R]ed globe light" anywhere on my dad's router, and there are no lights, on or off on the back of it. The lights on the front are:
WAN Ethernet (off)
WAN coax (off)
LAN Ethernet 1, 2, 3, 4 (all off)
LAN coax (off)
USB 1 and 2 (both off)
Again, there are No Lights on the back.
I did do all of the things you said in post 7, but this is still the state of things after coax is plugged in.
ONT is the Optical Network Terminal. The is the main unit where the fiber optic cable from the street connects. This will typically be on the outside wall, basement, or utility area in the house.
MoCA is the way the set-top boxes(STBs) communicate with the router over the coax wiring to get an IP address so the TV Guide and Video On Demand works. This is MoCA LAN(Local area network). The LAN is the internal network. The router gives out local IP address like 192.168.1.x to devices on your network like STBs, smartphones, and computers.
Verizon can provide internet from the ONT to router using MoCA WAN(Wide area network), but in this situation we are only dealing with the MoCA LAN.
The G1100 is the FiOS Quantum Gateway Router. I don’t know why but I just assumed the routers we were dealing with were G1100. From your description it sounds like you have the Actiontec Rev I. The lights that should be on are Power, LAN Coax, and Wireless. It is possible that the coax in the office is not connected to a splitter which is why the MoCA LAN light is not coming on. One way to check is you can take an STB from another room and connected in the office to see if the TV comes up.