I’m sorry to see you are hitting problems here.
I’m not sure why category pages aren’t working for you but, although I see you already did some troubleshooting, I like to repeat some steps that are well worth following:
- Please ensure your event plugins are up-to-date
- Deactivate all other plugins
- Switch to a default, unmodified theme such as Twenty Twelve
- Visit the Settings → Permalinks page (you need change nothing – just visiting this page clears up a set of rules used by WordPress internally)
Now test to see if the category pages are functional. If they are, please restore all of the other plugins/your theme – testing each time you reactivate one to see if any seem to be behind this problem.
Let us know how you get on!