This is due to mysql being in strict mode and not allowing NULL for dates which it does usually when not in strict mode. The solution is to have your server admin disable mysql strict mode. To do so please see this reference page: http://dev.mysql.com/doc/refman/5.6/en/server-sql-mode.html it involves a change to the my.cnf file or the way that mysql daemon is started. We have heard that godaddy does not allow turning off strict mode, but you can try complaining on a support ticket with them.
Magento does not work well either with MySQL strict mode it can cause other issues where NULL is used for certain tables that use date. The particular table for your reference is payperrentals_reservationprices date_from and date_to fields. These are set to allow NULL values but mysql strict mode still won’t allow it and inserts 0000-00-00 even when it should all NULL.