Log into your cPanel, click on phpMyAdmin. Once there, select the database your ZC installation is in, click on it. That will show you all the tables both on the left and more detailed on the right.
Now, click (on the left side) Categories. That will change your view on the right. Now click on "Browse". You will, then see all your categories listed (and man, what a list you have). Go to the bottom of that page, click on "check/uncheck all". Checkmarks will appear in all of the boxes beside each category listing......click on (on the bottom.....right beside "check/unckeck all") the little red "X". It will then ask you if you really want to delete.....it should look something like this (maybe without the 'zen' prefix):
Do you really want to : DELETE FROM `zen_categories` WHERE `zen_categories`.`categories_id` = 2 LIMIT 1;
DELETE FROM `zen_categories` WHERE `zen_categories`.`categories_id` = 3 LIMIT 1;
DELETE FROM `zen_categories` WHERE `zen_categories`.`categories_id` = 4 LIMIT 1;
Click on "yes". Done.
You will have to do the same for the table "categories_description", also.
You seem to have no products (done delete all of them?), so you shouldn't have to worry about the products tables.
BE VERY CAREFUL NOT TO DELETE THE WHOLE TABLE, JUST THE CATEGORY ENTRIES!! Don't think ZC will rebuild it.
Hope this helps.