Is your dedicated server on the same network as your computer?

If so, there is probably a routing issue. If not, most likely the hosts file on your computer got messed up, or you are having DNS issues. Basically, when you try to access their domain name, your computer/network/ISP sends the query to your own server, which responds (as it should) with your own web site.

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The best way to learn anything, is to question everything.