My host is also doing the PHP 5.4 update. When I tested my site I was getting a white screen.
I tried everything WordPress admin wise. What ended up being my problem was the .htaccess file. There was a lot of old references to earlier versions of PHP, Apache and a Drupal reference for some reason.
I copied over a .htaccess file from a different site that was working after backing up the old .htaccess file.
I got the fix from http://www.wpbeginner.com/wp-tutorials/how-to-fix-the-internal-server-error-in-wordpress/
