Let me guess ... you have the WAN port of the Netgear connected to the Verizon router and you've changed the LAN network address of the Netgear to be a different address range (such as 192.168.2.x)?
If so, the stuff on your Netgear is "behind" what we call a NAT/PAT firewall (the Netgear) and you're seeing the exact behavior that others on the Internet see if they try to talk to things behind your Verizon router.
If so, here's what you need to do ...
Disconnect the Netgear from the Verizon router. Change the IP address of the LAN interface on the Netgear to 192.168.1.222 (just some random number below 254 -- but for giggle, just use my suggestion for now). Make sure the DHCP server on the Netgear is turned OFF. Save the config (this will disconnect you from the Netgear!). Connect any LAN port on the Netgear to any LAN port on the Verizon router (LAN not WAN). Leave the WAN port of the Netgear disconnected.
Now ... reboot your PC's to pick up new addresses and see if they can see one another. Everything should be on the 192.168.1.x network.
If you are already configured this way, please provide a more in depth description of what's connected to what and the various configuration settings on the router so we can get a picture of what you have.