I solved this exact issue by getting a new WAN IP address for the router. That's why your cell phone workaround worked -- when you use your cell phone data instead of the router, your cell phone has a different WAN IP address.
My suspicion is Verizon has some of Verizon's own IPs banned from accessing the login server.
There are two ways you can get a new WAN IP for your router. If you are the kind of person that can log into their router, you need to get to the settings of your broadband connection and release and renew the DHCP lease.
If you aren't the kind of person who logs into their router, then you can get a new WAN IP by cutting power to the router. You'll need to leave it powered off for at least 10 minutes, but possibly even more. It could take a few hours or longer. You can leave it unplugged over night if that's feasible.
Make sure you make note of your WAN IP before and after so you're certain it has changed. You can log into the router to see your current WAN IP, or you can just go to google and search for "what is my IP address" and it will tell you. (The IP address is that series of four 1-3 digit numbers separated by dots. e.g. 171.23.69.2)
Rebooting the router won't work.
