I think the point is that we'd like to know how to find those pages of information that ARE available via a browser pointed at an IP, regardless of whether they're coming from the modem or a router.
Well, if that's the case, then you've already been provided the info you seek. If you need more or aren't satisfied, you should go to the appropriate mail list, forum, or NG.
In my case, if I have a "router" I don't know about it, because I have a box on my desk labeled "cable modem" and no visible piece of hardware labeled "router".
If the unit is listed as a cable modem, then that's what it is, although I'm not sure if some cable modems come with routing capabilities. I did a Google search for your specific modem (SURFboard SB3100, right?) and found http://www.gi.com/noflash/sb3100.html. I read anything that pertained to SB3100 and didn't see anything that mentioned routing. It did say that the unit supported networking but only if a network already existed, which sounds like it doesn't have any routing capability.
Since you mention it though, what IS a cable/DSL router and how would one know one had one, which model it was, etc? I can look right at the cable modem and read "SURFboard SB3100" but if I have a router no one has told me that until now.
I've a Linksys Etherfast Cable/DSL router. It functions as a hub for my network. It has 4 ethernet connections in the back of the unit. Using this router, I can access the internet using any computer on the network and using only one IP. It also acts as a DHCP network server and contains its own configurable firewall. You'll know if you had a router if it states so on the box and in the instruction manual. I'm thinking you think your cable modem supports remote configuration by using an IP address thru a browser. I don't think this is possible, at least with the unit you have. The only thing I saw that remotely resembled this was at the link I stated above: "In addition, the SB3100 features a useful web-page user interface that allows the cable service provider to monitor both the cable modem and the data signals coming in and out of the unit, which can be invaluable in diagnosing potential network problems." Keyword is 'cable service provider'.
In particular, being able to access these pages would be important if I ever need to call the cable-technicians out to my house again, because they tend to want to look at those pages, and they also have it written in our agreement somewhere that if you use linux, then you are totally on your own and they cannot guarantee they'll help you.
This is why I had them install my cable modem on a dual boot system. The technician was aware that I ran Linux dualboot throughout the network and wasn't going to touch it but at least I had Win98 for him to set up. Ron @ http://www.wigglit.com