You may have a diffucult road ahead, you need to upgrade all the way to 3.7.2 (or 3.7.3 which is going to be released soon).
Take a good look at the upgrade scripts (not only the SQL ones) and if you encounter an issue with one of the upgrade scripts (I remember the need to change one of them, but don't know which one exactly)
So
- back up your database and settings and templates (or everything for that matter)
- copy over a 3.7.2 distribution (or better 3.7.3 which should solve a nasty template bug)
- execute all the upgrade scripts from 3.3.4 to the next release and so on (yes quite a lot of them, but you have to)
- execute the upgrade scripts from php (here you may encounter the mentioned show stopper, but is a matter of harmless version definitions )
- clear your caches
- run eztc.php -s <siteaccess> - cross fingers and reload your site
Thanks for the post about the upgrade. We are about to make a decision to upgrade EZpublish from version 3.5.1. What is the current recommended version to upgrade to for a Production system? 3.6.x or 3.7.x?