At a guess, I'd blame one of the multiple Wordpress plugins installed to the account. I checked a few things including fixing an invalid permission-set on your public_html (it was set to 777 rather than 750) and renaming your .htaccess; neither fixed it, however renaming your index.php to index.php.bak and creating a new index.php with simple php code that returned "This is a test" worked fine - that indicates to me that the Wordpress install is trying to do something that is causing it to fail.
The best advice I have when situations like this come up is to backup the wp-config.php file and the database, and reinstall Wordpress from scratch, only adding the few plugins you need (preferably none). It's also worth noting that plugins that post to external sites, such as Facebook and Twitter, are known to cause issues because those services frequently blacklist our servers, and they're also against our Terms of Service due to their automation of third party services. These should not be used as a result.
