I also had this problem after upgrading from 1.4.2 to 1.6.1. I got the error when I click “Add to Cart” or when I try to edit and order in the backend:
Fatal error: Undefined class constant ‘PROCESS_MODE_FULL’ in /myserverpath/jlpowell1.6/app/code/core/Mage/Sales/Model/Quote.php on line 945
In my case the file app/code/core/Mage/Catalog/Model/Product/Type/Abstract.php was being overridden by a copy in app/code/local. I copied the core version to my local version, and reapplied the code change that was there previously.