When changing from a USB ADSL Modem to a Modem/Router (such as the DG834G), it is generally recommended that any software for the USB Modem is uninstalled. Otherwise, there can be problems.
The DG834G's own IP address will be 192.168.0.1 and it will allocate IP addresses to all connected computers using addresses between 192.168.0.2 and 192.168.0.254. Every network device (computer, games console etc) must have a unique IP address within that range.
Has the computer ever been used for "Internet Connection Sharing", because setting that up would give the network adapter with which you connect to the second computer the IP address 192.168.0.1 and you *WOULD* then have a conflict with the router's own address?