Step one:
Check the priority order of your network interfaces in the Network Preferences -> Active Network ports.
I'm guessing that you want the ethernet port to be above the dial-up (Modem) port.
Additionally, make sure your ethernet connection is configured using private class addresses (e.g. 192.168.1.x, subnet mask 255.255.255.0) and does NOT have a default gateway set. In this way, the Mac will route anything destined for the 192.168.1.x network over the ethernet port and everything else will drop to the next connection, namely the modem.
Check the priority order of your network interfaces in the Network Preferences -> Active Network ports.
I'm guessing that you want the ethernet port to be above the dial-up (Modem) port.
Additionally, make sure your ethernet connection is configured using private class addresses (e.g. 192.168.1.x, subnet mask 255.255.255.0) and does NOT have a default gateway set. In this way, the Mac will route anything destined for the 192.168.1.x network over the ethernet port and everything else will drop to the next connection, namely the modem.