That depends on how your home is set up. If you have a single device that has the wireless antenna (or antennae) and connects to the cable company then, yes, that’s the router. But it’s actually a wireless access point (WAP) and router in one device. And it’s the connection to the WAP portion that’s giving you trouble.
How do I tell? I have the router, and it’s “new” so I don’t know how to troubleshoot that.