Server and file problems
Check any other sites that you have on the same server, WordPress-powered or not. If those are down, is the server? Users tend to find problems before their hosting provider, but check with yours, who may or may not own up to a known issue. If you file a ticket, perhaps tipping them off, they may even tip you back with a downtime credit. Also check support and forum pages and, if there is one, your control panel server status widget.
Then again, did you make a server configuration change? If so, revert it and try again.
Had you been managing web files prior to the problem? Did you delete something or change some file or folder permission? Just a thought.
For any server type, check site and server logs for unusual activity such as traffic spikes, stopped processes, or changed file configurations, ownerships and permissions. Check that recent server logins were yours and that there are no new users in the /etc/passwd
file or for MySQL administration. If you suspect any kind of infiltration has occurred, then you should change all such passwords.
These latter tasks take time. Often it's best to address them once the site's back on track.