If possible, try linking your PC to your laptop with an ethernet cable (rather than wirelessly).
If you get proper access you'll know that the problem is with the wireless connection, rather than with the PC itself. (Try resetting the TCP/IP stack again or try another wireless adapter. The ones sold by Wilkinson's, at £10.50, are good but you can get other models cheaper on the internet).
If you still lose the connection using an ethernet cable the problem must be with your PC, rather than with the wireless connection. (Try reinstalling the network adapter, which you can probably get from the PC manufacturer's website).
If you continue to experience problems, it might finally be time to get rid of your XP computer and go for something a little more modern. I took that step a week ago and invested in one of these, which meets all of my needs easily:
http://www.accomputerwarehouse.com/product-info/cheap-windows-7-pc-lenovo-m57p-pentium-d-3-ghz-cpu-2gb-ram-80gb-hd
(Not exactly expensive!)