Site broken after failed 3.3.1 update

I attempted to do an automatic update to 3.3.1 (cannot remember from which version) and it failed. It just went to a blank screen after pressing the button to update. I then attempted to perform the update manually, using the instructions on this site as a guide. After doing that my blog is still not working. I just get blank pages no matter what page I attempt to access (including the admin pages).
In looking at the server log file, I noticed something that doesn’t seem right. Below are some entries from the server log:

[Thu Mar 08 15:46:49 2012] [error] [client 66.249.72.198] File does not exist: /var/www/vhosts/gizmoninja.us/httpdocs/category
[Thu Mar 08 17:20:39 2012] [error] [client 66.249.72.198] File does not exist: /var/www/vhosts/gizmoninja.us/httpdocs/2010
[Thu Mar 08 16:01:20 2012] [error] [client 66.249.72.198] File does not exist: /var/www/vhosts/gizmoninja.us/httpdocs/2011
[Thu Mar 08 16:04:34 2012] [error] [client 66.249.72.198] File does not exist: /var/www/vhosts/gizmoninja.us/httpdocs/page
[Thu Mar 08 17:07:42 2012] [error] [client 66.249.72.198] File does not exist: /var/www/vhosts/gizmoninja.us/httpdocs/tag

It looks like something is causing folders to be looked for in the wrong location? I know the 2011 and 2010 folders are located in /wp-content/uploads/. I’m not really sure about category, page and tag, although I believe there are php files named as such.
Am I looking at this correctly? If so, what do I need to change in order for these folders to be looked for in the proper locations?