OS X :: Absolutely Perplexed - Strong Airport Signal But No Internet

here's the run down: today I moved into a new place with two roommates. They have a wifi internet connection set up (modem + dlink router). I have been given all of the info regarding log ins and passwords. My Airport is telling me I have perfect reception and that I have a very strong signal. Yet, there is no internet (when I open Safari it tells me I am not connected to the internet). I've had this problem before, but it is usually resolved by restarting the modem or the router, by restarting my computer, etc. And here's the kicker: I am using, right now as I type, someone else's wifi connection... yet I accessed it with the same password. It's a very basic password (12345). I thought maybe this was our unit's connection, but I actually unplugged the modem and continued to use the internet with this connection. The problem is that this connection is very slow and rather useless. I'm actually able to use 3-4 of these with the same password (12345). One of them is called 'dlink,' the name of our router. But our connection is supposedly under 'Nicks,' my roommate's name).