Restart your computer, in case a configuration setting somewhere has gotten messed up.
At least in Windows, I believe that if a site is inaccessible more than a few times (or a few minutes or longer), that situation is remembered, and the system quits trying until the TTL (time to live) of the last response has expired (about a day). I've encountered that, and a system restart fixed it. Clearing the local DNS cache probably also would, but I don't remember how, and not on OSX.
It's also possible that browsers might do the same thing. It might be worth clearing your browser cache, even though that wouldn't directly address this "remembered inaccessibility" thing.
Then, if still a problem:
Check your "hosts" file for entries mentioning your website name.
If you have a ping or tracert (trace route) tool, try tracing the route to the IP address directly to check the path.
Try changing your DNS service provider, such as to something like OpenDNS.
Some of the underlying questions are:
Are you getting a correct IP address in response to DNS queries for your site?
Is your computer (and firewall, and ISP, and antivirus, if any) permitting traffic between you and that IP?
Are your browsers blocking traffic to/from your site for some reason?