This should be a simple upload and installation of a new theme, something that the average blogger can learn to do in 20-30 minutes.
However, it looks like you've left your WP core and theme updates for so long that you're starting to crash your site.
My suggested remedy:
-back up all data from the database
-create separated files of all important pages
- turn off all plugins
- load theme normally, and attempt to install
-if theme doesn't install, then we may need to install an older version of WP core
-once new theme is installed, we update WP core if applicable, start checking the site for issues, and turning on plug-ins
* If you've thoroughly buggered it up, we can do a clean install and use the separated created files to recreate the site manually. This may take a bit longer. I suggest that your own people can do the creation of separated files on one of your office computers, and re-enter the data after the new install.
I will need WP admin privileges, and cPanel access may also be required.
I've entered a minimum bid because this is something that should really only take a few hours if your staff have properly separated the important data. Keep in mind that if the database gets screwed, you could lose everything and have to start from scratch. We want to avoid that situation if we can.