I have a strange issue.
Not possible to create new subcategories. Deleting existing works fine.
Creating new ones gives error 404.
Tried to reinstall Magento, same problem.
Error file, does not give any reasonable answer.
All other functions are working fine.
Which URL do you see when you get the 404?
Did you tried disabling all extra modules?
Can you share the no reasonable messages from your logs?
I'm sorry but without an error message I'm not sure how to help.