Erm. I'll try to explain this as best I can without getting too technical. Basically, what it boils down to is that your lovely DSL modem is actually also a router. These kinds of combo devices are referred to as "gateways." (Actually, lots of people have different names for everything, so nomenclature won't be universal everywhere. Life sucks that way sometimes, but that's what I'm going to call it here.)
Routers in general set up their own little private network ("private" meaning "having its own little IP address space that's not unique to the internet", see
http://en.wikipedia.org/wiki/Private_network). They also set themselves up as the lord of their own little domain, acting as DHCP server (meaning they for any computers or devices that are hooked up and paying attention, the router will provide the IP address and DNS info and all that information automatically).
The issue, in your case, was you had two routers attached to each other that were both trying to lord over the same private network. Long story short, that doesn't work very well. Under normal circumstances, you'd ideally tell your wireless router "OK, stop being a router and just be a wireless access point for me." That way, you'd have no conflicts and life would be good.
Your router, unfortunately, doesn't give you that option. So, what I had you do was create a second private network INSIDE the first one that your wireless router could be happy in. This will work fine for your standard internet usage. However, you're likely to have issues with any program that wants incoming connections, due to the obnoxious complexity of the setup. This means online gaming, bittorrent, and direct file sends via IM clients are all likely to get cranky. Without actual hands-on access (or better documentation for both gateway and router), I'm not going to be able to help you with that. Actually, if your hardware is limited enough, the proper solution might be "buy better hardware."
Oh, one more thing - networking is acronym-heavy. Get in the habit of looking up what those acronyms mean, and things might start to get a little less fuzzy more quickly.
Hope this clarified things a bit!
Why yes, my shift key *IS* broken.
