What I meant was...run "cmd" (or "command" in Windows 9x) on the one with the wireless adapter, then at the command prompt, type "ipconfig". As Ernie mentioned, it should have some address like 192.168.x.x.
Try to ping the router :edit: from the machine with the wireless adapter :end edit:, if you know its address (probably 192.168.0.1 or 192.168.1.1). This will be the address you use to get into the router's setup, if it provides a web interface for configuration (I haven't used Belkin routers, but every other major router brand works this way, so I assume they do, too). If you can ping the router's IP address, that means that the router has let you onto the network and should have given you a valid IP address. If this is the case, that is good, then try to ping www.google.com.
If you are able to ping the router but not google, then it is more than likely just a router configuration issue (i.e. look thru all the settings in the router for things pertaining to wireless connections).
Like I had mentioned before, I recommend you disable WEP. Also, disable WPA or any encryption or authentication for wireless devices just to get everything going. This will help isolate the problem. You need to disable it in both the router and the software on the machine with the wireless adapter.
I have run my laptop even with a "low" signal strength, so if it has some kind of signal, then signal strength should not be a problem (it will just affect performance).