Use tools like tracert to verify you have an internet path from your workstation to your web server. There may be some internet outage between you and them that's causing the problem. Also if you can check from a different location using a different internet provider.
Another possibility is your host is having some major problem at their location.
I'd start with a command line and first do nslookup on your url, make sure you get the IP resolved properly and you don't have a DNS problem.
Next I'd run tracert to your url and see if you can get to your site IP. Sometimes you won't see your final IP on tracert though, so it's better if you've run tracert in the past and know what results to expect.
If these tests pass you may have some malware/virus on your machine causing problems.

What's the name or the url of your webhosting company?

Thanks everyone. The problem appears to have resolved itself.
I may look at getting alternate nameservers in case this happens again.