Silly question ... you did check the base station of the cordless phones and/or the handsets to make sure no one flipping a switch to turn the "ringer" off didn't you?
Do you have POTS (wired from pole) or FIOS phones?
I had a similar problem with my old POTS line. It would ring very briefly on an old bell ringer phone but would stop a second later. It would not ring on a cordless phone on the same line, but you could answer it if you heard the very brief ring. The problem was found to be a defective switch unit in a distribution box a block away. The phone system checks for a certain load on the line when it is ringing and if it isn't right it will stop the ring voltage. Most digital cordless phones wait a second or two before ringing. The phone company (Verizon) told me it was probably caused by too many phones on my line, so I disconnected all but an old non-electronic one and connected that one to the box outside my house. That way they couldn't blame the house wiring. Once a tech arrived and I showed him the situation, he knew exactly what top do and drove down the street and fixed it 15 minutes later.
Another possibility : Did you recently add any phones? If so, try unplugging them one at a time and have someone call so you can check to see if that had any effect. If one or more of the phones or an extension line have problems , that can stop the ringing too.
Instantaneously my corldless phones stopped receiving calls, lost dial tone, and could not send a call. All the land line phones in the house work well. I connected the cordless phone to the ONT box and it does not work there either? Do I need new cordless phones. I have two and they function on two different base chargers.
I'd say if you plugged the base station into the ONT directly and it still didn't work, then either your handheld units have lost touch with the base station (check your handset instructions for pairing the handsets with the base stations so that they have the same security code, etc. -- if the phones somehow lose contact with the base station, they will not longer have dial tone, etc.) or the base station itself it shot and you need to replace it.
The fact that the other phones continue to function means there is dial tone coming from the ONT so it's not a Verizon issue.