With a x-over cable in the equation, are you connecting the WIN7 NIC directly to the Server2003 NIC?
Do you have link lights on both NICs? You may need to check that the X-over cable is connecting on all pins.
The Win7 machine will need to have the Win2003 NIC as it's gateway. This is true whether it's a direct link or via a switch.
The server & client both need to be on the same subnet.
Routing needs to be enabled on the Server2003 to allow traffic between the 2 NICs.
Good luck.