Upgrading is unfortunately not as simple as replacing the war file. You need to read the upgrade notes for all of the versions above the one you are on, up to the target version. These provide information about new requirements or changes that you need to be aware of.
Prior to 2.31 they also contained upgrade scripts to be run on the database. In later versions the war file contains these upgrades and they are applied automatically. If they fail, the database is left unchanged and the system fails to start. I think that is the behaviour you are seeing.
Once you have followed the upgrade notes, you should be able to run your upgraded system. If you have problems at that point you may have to share the errors from your tomcat logs in order for us to help you out.
I hope that helps to point you in the right direction.