Is my router going bad?

Make sure your router is pointed to the correct default gateway address which would be the IP address of your modem that it's connected to. This is the problem with most connectivity issues. Once that has been settled you should have no further connectivity issues with the router getting out to the internet. Another possible solution would be to configure your desktop PC with a static IP address with it pointing to the default gateway which would be the IP address of the router itself. The best way to do that would be to go to the properties tab of the Network connection on your PC click once on TCP/IP select properties then configure the network adapter with a static IP address using the first three numbers of the default gateway then a number of your choice on the fourth. Example if your default gateway is 192.168.0.1 then choose an IP address of 192.168.0.x with x being a number of your choice. Hope this helps