When you say "internet sharing" if you mean Windows ICS (Internet Connection Sharing), you basically have two computers, one that has two network interface cards. One card (NIC1) connected to the LAN and the other (NIC2) to be connected to the other computer. In this configuration, on your main computer, you enable Internet Connection Sharing. The cable you use between both computers is a cross-over cable. Computer 2 then configured for networking using its NIC has no special configuration. It receives an IP address and the rest of its TCP/IP config from Computer 1. For you to be able to access the internet from Computer 2, Computer 1 must be powered on and ICS services must be running.
Alternatively, rather than setting up this configuration, why not have a hub or a switch connected to your Internet router, and just plug in computer 1 and computer 2 into the switch ports so that each computer has its own connection to the local area network. ICS would not be required in this case and each computer operates independently.