if you bought the nintendo wifi USb dongle, there's no reason
why it *shouldn't* connect to the xp machine downstairs.
wireless can be affected by other devices in the house such as
tv's, microwaves, DECT phones, radiators and double glazing.
another option is to get hold of the nintendo LAN adaptor which
also connects to the rear of the Wii via USB. you could then get a
couple of "home plugs" which are ethernet devices which plug directly
into your electrical sockets / outlets. in effect, they use the electric
mains to transfer the network data around your house.
you would need 2 of these...one near the xp machine and one near
alternatively, either get a wireless router, or get a wired router and
run ethernet cable up to the Wii.