Had the same problem between my PowerBook G4, a Belkin F5D7011 WiFi Card and a Linksys WAG54GX2 Router. Now fixed it
Mac OS X supports WEP, WPA, WPA2. But the encryption used varies from those found on non-Apple Wifi kit - (WPA2 Personal works fine with an Apple Airport Base Station).
Hence, "WPA Personal" on the Mac corresponds to plain WPA, with a pre-shared key (PSK) and TKIP encryption, on non-Apple wireless routers.
I was trying to use "WPA2 Personal", and could connect to the router with a strong signal, but no Internet. Changed this to "WPA Personal" and with TKIP encryption, and it works quickly.
The Belkin WiFi card is a "F5D7011" (Ver 1212UK). It uses a Broadcom chipset, which is what the Airport Extreme cards uses. Mac OS recongises it as an Airport Extreme card. So connecting with 802.11g speed.
TTFN,
Rich