I've read that people have hardwired to Fios router and its "plug and play"
People are pulling your leg. "Plug and play" was terminology introduced by Microsoft for PC products. Apple is not Microsoft and the Time Capsule is not a PC product. Nothing about a Time Capsule is plug and play......it must be reset back to factory default settings and then set up to work correctly with another router, like Fios or any other brand.
We asked for the model number of the Time Capsule.....and gave you instructions on how to find it.....but still don't have that information, so we are forced to proceed with limited information. Please understand that even with a correct setup, there are no guarantees that things will work if you are planning to use the Fios wireless network to back up your Mac(s) to the Time Capsule.
Check to make sure that an Ethernet cable connects from one of the four LAN <--> Ethernet ports on the Fios router........(there are likely 4 of them, choose any one that you want) to the WAN "O" Ethernet port on the Time Capsule (TC). This cable must be connected permanently at all times.
Power up the TC, if it is not already on, and let it run a few minutes.
Hold in the reset button on the back panel of the TC for 7-8 seconds, then release
Allow a full minute for the TC to restart to a slow, blinking amber light status. This will confirm that the TC has been reset correctly, so it can now be programmed with the correct settings that it needs to connect to the Fios router

Next, click on the WiFi menu at the top of your Mac's screen
Look for a listing of New AirPort Base Station
Click directly on AirPort Time Capsule just below that listing. Your screen may simply read Time Capsule, since you have an old model

When you click on Time Capsule, that will start up the AirPort Utility setup "wizard" automatically. The wizard will take a few seconds to analyze the network settings and then display a window that looks like the example below, except that you will see a Time Capsule pictured.

Network Name.......Type in a short simple name for the TC WiFi network. Later, we will turn off the wireless on the TC, unless you want to have another WiFi network.
Base Station Name.......Type in a short simple name that you want to call the TC as a device
Password.......Type in a password that will be used for the Time Capsule
Verify......Type in the same password again to confirm
Click the Next button at the lower right of the window
The "wizard" will now set up the TC with the correct settings that it needs to connect to the Fios router. When you see the message of Setup Complete, click Done.
At this point, the TC should be visible in AirPort Utility.
Post back on your progress and we will continue.