Thanks for all the help guys. I think I was a bit stupid to buy this router in the first place

. However, a couple of questions:
First off, although my modem has only one ethernet port (a physical problem) could this be overcome by using some kind of 1 to 2 ethernet splitter? Or is there some kind of technical problem prohibiting this? And if this is possible, would this still cause the same security risks?
Second, assuming the above is not viable, and I reason that the minor risk of someone finding my new ssid, spoofing a mac address and cracking my WEP on a whim (not sure if the firewall on the second router would have anything to say about this, however) is worth taking, how exactly do I set this up? There are 5 ethernet ports on both of my routers. My first router has a cable from the modem plugged into the yellow port, labelled 'modem', with another cable running from one of the computer-labelled ports into my wired computer (my laptop connects wirelessly). My question is, where do I connect my new router? I assumed it came from another one of the computer-labelled ports and went somewhere into my second router. But which slot does it go into? Does it go into the port that SHOULD be filled by the modem cable (if I was doing things traditionally) or into one of the computer-labelled ports? Either way, I tried both and the connection is still labelled as 'Not Connected'. And, I also tried messing with the 'access point' settings, not really sure what I was doing. Considering I only need it for one limited device, I reasoned maybe that would be enough. But still, no internet.
Finally, IF I somehow manage to set this up, will I notice any effect on my current connection? As mentioned earlier, I did notice problems with my connection when I had the new router connected (although this may be due to incorrect settings or something). I obviously don't want that.
I've posted my problem on a few forums, and this one seems the most helpful

*sigh* Way too much effort for a stupid little Nintendo DS
I thank you all.