It sounds suspiciously as though the router isn't connected correctly, so that your public IP address as allocated by the ISP is being passed to the first PC to connect. The second PC cannot get an IP address and so cannot get online. The *router* should get the address allocated by the ISP and, in turn, allocate addresses to the computers connected to it using one of the address ranges reserved for Local Area Networks, most commonly 192.168.x.x addresses.
Are you using a Cable/DSL Router with Virgin's Cable service and connecting the Cable Modem to a LAN port instead of the WAN port? What IP addresses do the two PCs have when you try to connect simultaneously?