Wireless Network connected but no internet

I am very unfamiliar with wireless connections and just got a computer with
one. it's a laptop running xp. there are several wireless connections that i
can see and connect to for free from my apartment, and in the toolbar on the
lower right corner, it shows that I'm connected to the strongest available
connection, which is an unsecure wireless network. However, when I then try
to go online, it doesn't connect. When I'm at work, I connect through a
network cable, so I'm guessing there's just some setting I'm missing that's
keeping it from connecting. We have another laptop at home and it connects
easily to the wireless network.