May I ask why you want to do this?
When I read you question a Web Server instantly comes to mind, but that is because I am an IT guy.
If you had a domain name, and a provider that let you use their DNS servers and point the A record of your domain to your web-serve'rs IP you would technically be doing what you want.
I say it like that because I don't want to be rude and come off acting smart, and say all web servers are computers with files and folders on them. Which turns me around to my initial question.
Why do you want to do this? (simply curious)
Your computer has to be accessible across the internet. Most commonly using Apache. A lot basic of ISPs block port 80's incoming traffic so setting up a web server using an ISP that simply serves internet may be difficult without port forwarding.
Last edited by stevenmw; 10-12-2012 at 02:37 PM..