Solution 1. Connect it to internet using your internet connection. It will assign an IP address to your machine. But it will keep changing everytime you connect /disconnect
Solution2: Find a hosting company, which can host your machine in their datacentres. This will give a permanent IP.
Install Linux on your spare PC. You need a IP address from your ISP. Configure your PC with the IP address so that it can be found on the net. Too long to explain. Go to http://www.aboutdebian.com/internet.htm