Hi,
I have had similar issues. Two things, the 'All in one event calendar' is a resource hog and on low end hosting will kill the site by pushing the CPU resources to 100%. Wait for version 2 which is due out this week or next. Second turn off database and object caching, and do not use Minify on Auto (set to manual and tune it). If you cannot get into your backend then use phpmyadmin to remove W3 and the calendar from the active plugins. Don't forget to change the index (seen below as a:21) or all your active plugins will become inactive. Below is part of my active plugins in the options table:
a:21:{i:0;s:19:"akismet/akismet.php";i:2;s:19:"bbpress/bbpress.php";i:3;s:41:"better-wp-security/better-wp-security.php";i:4;s:25:"bigcontact/BigContact.php";i:5;s:19:"captcha/captcha.php";i:6;s:29:"font-resizer/font-resizer.php";
...
i:18;s:33:"w3-total-cache/w3-total-cache.php";i:19;s:24:"wordpress-seo/wp-seo.php";i:20;s:27:"wp-crontrol/wp-crontrol.php";i:21;s:29:"wp-mail-smtp/wp_mail_smtp.php";}You may have to clear out htaccess as well.
Hope this helps