Wow that is fucking bizarre.. this isn't using powerline networking (ethernet over your power system via little wall sockets) or anything like that is it?

I'd definitely start with a factory reset of your router. Some routers have a little pin you need to hold down with a paper clip. With others you'll have to do it from their web interface...

You can usually get to the web interface by entering your default gateway in a browser. Something like http://192.168.0.1 or http://10.0.0.1 are common. It might be written on the back of your router. You can also usually find your default gateway in your connected network settings pretty easily: on my android phone it's just called "Gateway".

Once you're in the web interface you'll probably need to put in login info which is almost always written on your router. Then navigate that hellscape until you can do a factory reset.

Also if you're in the US and have a router provided by one of the big ISPs like Comcast, Verizon, Frontier, etc you're almost certainly renting your router for like $10 a month from those bastards. So call them up and make them fix it or get you a new router if they can't figure it out. You might as well try this before spending money buying a router. I saw your other comment that you've actually bought this router yourself. Resetting it might be slightly more tricky since you might need to configure the modem settings a bit, but it's usually pretty easy. Probably worth looking up and downloading a pdf of the manual for your router before you reset it though in case you need to read it without internet.