Start again from the beginning (and I'm assuming that you are using XP in both computers).
In the "Host" PC, the one connected to the broadband modem, open the Network Connections folder, highlight the actual internet connection (the modem connection), right click it, select Properties and then the Advanced tab. Tick the box "Allow other network users to connect through this computer's intenet connection". Then click OK to close the dialog box.
If you now highlight the Loal Area Connection and look at the very bottom of the blue pane on the left, it should show the IP address as 192.168.0.1 and that it was "Manually Configured".
Now, open the Network Connections folder in the "Client" PC, highlight the Local Area Connection and look at its IP address at the bottom of the left blue pane. It should have a different IP address, but in the SAME range of 192.168.0.x and it should show that the address was allocated by DHCP. If this is not the case (and it has an address of either 169.254.x.x or 0.0.0.0), double click the Local Area Connection, select the Support tab and click the Repair button. This should force it to renew its IP address and it should get a correct address in the 192.168.0.x range from the "Host" PC, which acts as a DHCP server.
Does that get you any further forward?