Your router needs to get an ip address via your modem from verizon. Since you're able to connect directly through your computer, apparently your modem is providing your computer with the ip address.
First you need to turn off the router and the modem, you need to turn off the modem because it is now talking directly to your computer and that address needs to be changed.
Then turn on your modem, wait a few seconds and turn on your router. Your router should ask the modem for an ip address, if it does not get the address from the modem it will not work correctly.
Since I am not familiar with your router, it is best to call your router manufacturer to ask for assistance in resetting the router to automatically request an ip address from the modem. They will probably have you reset the router so see if you can do it first. If that works you will have to reset your wireless configuration to secure your network.
It sounds like verizon is not doing anything special such as asking for passwords, etc, so that would not be causing any problems. The modem manufacturer should be able to help, if not ask verizon for help.
I do not believe the router is not fried but your comm port may have been fried if the outage caused a surge. The router manufacturer should be able to help you determine that. I think just your settings need to be reset but on the slim chance it was fried the manufacturer should be able to tell you.