You should still be able to run IIS as long as you do not allow anybody outside to access it through the cable modem. For instance, if you have IIS for your own private development or testing purpose, it should not violate the service agreement. However, if you let public access your web server, then you violate the service agreement. The technology to detect what kind of webserver running on your site is very simple.

Router is a completely different thing than a server. ISP may be able to determine you are using a router, depend on the implementation of the router, but they have no way to tell whether you have more than one machine connected behind the router.