Network routers, modems and such are susceptible to power surges. It is possible that all or some of the ports on the router were damaged. I have seen it happen. Wireless works fine, but, all the ports dead.
Can you connect directly to the modem? If you can and if you get a good connection then you'll know that the router ports are bad. If you don't get a connection then the problem is in the computer.
Judging by a problem with the monitor I would bet the problem is the computer.