Hello,
You could use the export tool to export your data.
Then clean out your alfresco install - drop and recreate the database and remove the alf_data folder.
(You might want to do a seperate deployment to ensure you don't loose any data if something goes wrong - copy your existing alfresco database and tomcat dirs so you can rename them back if something goes wrong - although it shouldn't).
Once you have a fresh install, with working categories, import your previous export and you should have all your data back.
Hope this helps,
Steve