The laptop certainly won't be too old - I can use a Belkin USB WiFi adapter in an older laptop running Windows 98SE and with USB 1.1 ports. Your ports won't be USB 1.0 (1.5Mbps), but rather USB 1.1 (12Mbps). Do the ports work with other peripherals - printer? scanner?
Try uninstalling all of the Belkin software and run System Restore back to before you originally installed it. Reboot the laptop and plug in the USB adapter. If Windows "finds new hardware" select the option to install drivers from a specific location and navigate to the Drivers folder on the CD, select the .INF file. If the CD automatically starts for you to install the Belkin software, exit from it. You can then use XP's own wireless networking software which is better.