I've solved your problem.
First, you'll need PHPMyAdmin or a similar tool which allows you to edit your database. (download it from http://www.phpmyadmin.net/home_page/downloads.php
). It is very easy to set up. Just extract the downloaded file into your web directory (eg. http://www.mysite.com/phpmyadmin/
), then point your web browser to that directory.
Next, click on the dropdown list on the left of the screen, which says "(Database)...". Select your database (eg. mambo). Next, select "mos_categories" which will now appear on the left of the screen.
Along the top of the screen, there should be several options, including "Structure", "Browse", "SQL", "Search", etc etc. Click "Browse".
Search through the list of categories until you find the category you created in "Manage Event Categories". This will be under 'Title'. It should have "com_events" in the 'Section' column. eg. The category I created is called "Birthdays". Under title will be "Birthdays", under section will be "com_events".
Once you've found the category, click on the small icon of a pencil and paper (in second column). Now, look down through the table until you see a row with "published". The value will read 0. Change this to 1.
Presto! There you have it.
This may seem very confusing, but once you've gone through it once, it's as easy a pie!