It works with wi fi because when you connect it is a new connection so it sets it up OK.
But you are confusing your modem becuase when you unplug the cable from your computer it still "held" the network connection.
When you then plugged it into HER computer the modem still though ti was talking to YOUR computer.
The quickest and easiest way to get round this is to power down your modem and her laptop for a few minutes, then turn on the modem, then turn on her laptop.
That may work.
If not the other option is to go into the networking of XP on her laptop and disable the network, then enable it again.
A BETTER solution in the long run is to get yourself a wireless router.
Then you can leave your PC plugged in, AND your friend can also connect to the router via wi fi, and you can BOTH use the interent at the same time.