Internal Server Error

My site is not accessible. I received a couple of errors in the error log that goes something like this.

[14-Sep-2013 06:47:16 UTC] PHP Fatal error: Call to a member function get_active_modules() on a non-object in /home/filipin2/public_html/wp-content/plugins/jetpack/class.jetpack-heartbeat.php on line 76

[17-Sep-2013 06:47:35 UTC] PHP Fatal error: Out of memory (allocated 12582912) (tried to allocate 30720 bytes) in /home/filipin2/public_html/wp-includes/rewrite.php on line 1676

[19-Sep-2013 15:32:01 UTC] WordPress database error You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ” at line 1 for query SELECT count FROM wp_term_taxonomy WHERE term_id = made by require(‘wp-blog-header.php’), require_once(‘wp-includes/template-loader.php’), include(‘/themes/mesocolumn/front-page.php’), get_template_part, locate_template, load_template, require(‘/themes/mesocolumn/lib/templates/home-feat-cat.php’), dez_get_cat_post_count

I’m not quite sure if these are the problems because these logs are dated in the past and my site just went down a couple of hours back.

Hope someone can help. thanks!