Certainly do not install any Virgin software! - rule number zero, never let any ISP's software anywhere near your computer.
If you've got the Virgin modem plugged straight into your PC then it's your PC's MAC address that is the only PC that Virgin will talk to, and the only one they'll give an IP address to, because they only give out one IP address.
You'll need to buy and install a router with NAT and DHCP server capabilities - connect that to your modem, then connect as many PCs as you like to the router. (There's probably some messing around needed to get your router to connect in place of the one PC you've had connected so far - just leaving everything switched on overnight and power cycling the router and modem a couple of times might do it.)
I use a Linksys BEFSR81 but there's plenty of choice these days.
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Sorry, the above is assuming you want to use both machines at once. If you just want to use one at a time you can simply switch between them, but you'll probably have to wait a while for it to start working each time you switch. Like I said, overnight will probably do it, but if you're in more of a hurry than that "four hours" rings a bell.