Mike,
Just to make sure, the steps below are for Joomla 2.5. If you're using Joomla 1.5, let us know as the steps will be different.
The main thing you want to check in the database is the jos_extensions table. Look for the 'plg_authentication_joomla' extension in the 'name' column. Make sure the enabled and access columns are set to '1'. Do the same for the 'plg_user_joomla' extension.
Alternatively, you can try running the following query. Always make sure you have a backup first before running queries that anyone suggests

UPDATE `jos_extensions` SET `enabled` = 1, `access`=1 WHERE `name` = 'plg_authentication_joomla' OR `name` = 'plg_user_joomla';
Hope that helps,
Alex