This site is running WP v 2.2.1 which is very outdated and insecure as of this date...You will need to do a few things...
1. Backup all site files and the MySQL Database first...this is critical...
2. Manually update WordPress...this is important to do properly:
A) only upload the following folders from a WP3.4.2 download:
wp-content/themes/twentyeleven (NOTE: if this folder already exists, skip this folder)
B) rename the folder wp-content/plugins to wp-content/old-plugins (this will disable all plugins which are likely too old for the current version of WP)
C) Rename all folders, except the twentyelven folder, found in wp-content/themes to old-theme_folder_name (this will force WP to use the default unedited theme you uploaded).
3) Contact webhost and make sure the server env is running the required versions of PHP and MySQL.
4) Run the site - once logged in, you can update theme and plugins, clean up database etc...
(don't forget that site backup!!!)