Are you 100% sure you're pulling a useable IP address? Check your router settings and make sure it's assigning one, though I'm sure you've done that already.
I had to help a friend who had MAC filtering on his router, so it would say it could connect, and for whatever reason it showed "connected" to the router, AND he was being assigned an IP, but it wouldn't allow him to *do* anything. Not sure why it assigned an IP in the first place. If you have MAC filtering on your router, try disabling it? **edit** or, make sure to add an exception for your droid phone, you can get the MAC address from the wifi settings advanced screen (see later in this post for how to get there) but your router should see it automatically if you try to connect.
Or, just to debug, temporarily turn off all security on your router, try connecting, and if it works at least you know it's related to your router's security settings (WEP/WPA/WPA-2 etc) and not the phone itself, or at least you can narrow it down to how the phone and the router are interacting re: security.
Another thing to try: if you go to home, soft menu key, settings, wi-fi settings (where it has Turn On Wi-Fi toggle), click the soft menu key, go to advanced, and set it up to use a static IP. Perhaps that may work?
Or, maybe there's a DNS issue. So you could try using a static IP, and then setting up one of the openDNS servers instead of your ISP's.
Not sure your technical level of expertise so I'll subscribe to this thread in case you have any questions about the above.
Sorry to just throw random things at you, but I figure every little bit has a chance to help
