I have found connecting devices via crossover cables can cause problems due to LAN speeds not being negotiated correctly. I would try setting the LAN cards on both machines to say 10mb/s half duplex or get hold of a cheap hub. A cheap hub should cost less than PC world charge for xover cable, 15quid ish.
The cable must be working in one direction as your are picking up packets from 'kids pc' on your PC. If you reverse the cable & same happens then cable should be OK & probably a duff LAN card.
i found a page on the web that told me netbui is often beter for cross over n/work than tcp/ip on its own also that netbui is no longer installed as standard under xp and that you have to copy the files manually into the right folders on your puter
i can ping have still got tcp/ip ticked though and have just tried unticking the netbui protocol and connection is still good? so maybe it wern't that after all god knows. but its all happy at moment, and when my lad gets home from twi kon do were going to have a bit of a death match