Thanks. I should have said I am using WinXP Zero configuration service. No other software. Everything works fine if I turn off WEP. But it doesn't work if WEP is enabled. So the network itself is fine.
I've got all updates, including the SP1 rollup, the Wireless rollup, the Security CD that Microsoft mailed out, plus all other critical fixes.
I am using a Buffalo router (WBR-G54) and Buffalo Adaptors (WLI-USB-G54). It doesn't automatically provide keys. I have to enter it in. I have tried Hex and Ascii keys.