The problem is that your "client" PC isn't getting its IP address from the "host" PC's DHCP server. Windows is almost certainly allocating an address in the 169.254.x.x range which won't let you connect to the "host" and definitely won't allow internet access.
Make sure that "Internet Connection Sharing" is still enabled on the actual internet (modem) connection in the "host" PC and that its Local Area Connection has the fixed IP address of 192.168.0.1 and subnet mask 255.255.255.0
To enable “Internet Connection Sharing” in Windows XP, open the Network Connections folder, right click the actual internet connection (modem connection), select Properties and then the Advanced tab. Tick the box “Allow other network users...etc”.
The "client" PC's Local Area Connection should be set to get its IP address automatically, which it does (or should do!) by DHCP from the "host" PC.