Originally Posted by Loulabelle

I'm going to guess that you've got maybe a DSL router so you're only using the switch part of it so that's not going to cause any problems unless it is acting as the DHCP server. Is the Linksys router acting as a DHCP server? If so that might be the problem, from what I remember of internet connection sharing the main computer (the one with the modem and internet connection) acts as a DHCP server and assigns an IP address to the system wanting to share the connection. You might also want to check that both computers are set with the same workgroup name...... by default MS sets it to WORKGROUP but if one has been changed it can cause probelms.
Hope that helps )