I have tried both LAN ports on the VZW Gateway
Thanks for the screenshots. This really helps. LAN ports are labeled with a symbol that looks like this: <-->
The (Time Capsule) tower has four (4) ports into which the Ethernet cable fits; is there only one (1) that is the "RIGHT" one? If so, do you know which one is the "right" Ethernet port?
The WAN port, which is always marked with an "O" is the correct port. This is the port at the bottom of the row of ports on the back of the Time Capsule. You have the cable plugged into the correct port on the Time Capsule in the picture that you posted.
"Waiting for an Ethernet cable to be plugged in..."
AirPort Utility is not detecting the Ethernet connection. Here are the possible reasons:
Often....it is a bad Ethernet cable......try another Ethernet cable
The LAN port(s) on the Verizon gateway may not be active. Check the Verizon gateway manual to see if there is a setting or option to enable the Ethernet ports.
If you have a computer with an Ethernet port on the device, you can check to see if the Ethernet connection is working by temporarily connecting an Ethernet port from one of the LAN <--> ports on the gateway to the Ethernet port on the computer.
Turn off the Wi-Fi on the computer so that it will use the wired connection. Check and see if you can get a good Internet connection that way. If you can, then you know the Ethernet port on the gateway is working and the Ethernet cable itself is good.
If you cannot get a good Internet connection when you are running this test, then try another Ethernet cable to see if things will work that way. If they do, you know that the previous Ethernet cable was defective. This happens quite frequently.
If things still do not work with the second Ethernet cable during the test.......(it is highly unlikely that you would have 2 defective Ethernet cables).......then the LAN port(s) on the gateway have likely not been enabled or they are defective.
If you find this to be the case, then you will need to check with Verizon about why the Ethernet ports are not working correctly.
Now, if you can get a good Internet connection when you run this test using computer, then that tells you that the Ethernet port(s) on the gateway are good and the Ethernet cable is good as well. You can now connect the cable to the Time Capsule and turn the Wi-Fi back on at the computer.
When you connect the Ethernet cable back to the WAN "O" port on the Time Capsule watch carefully to see if a very small green light appears next to the port. If it does, this means the port is working. If the light does not appear when you connect the Ethernet cable, then you may have a defective WAN "O" port on the Time Capsule. This is very unusual, but it is possible.
If the WAN "O" port on the Time Capsule is not working, things get more complicated and we will have to try some other workarounds.
Please post back on your progress.