When I launch StarReminder I get an "Invalid database format or database corrupted" message.

This error occurs because your database has been corrupted due to an instant electrical power loss or an abnormal program termination.

In order to fix this you must locate the latest database backup file and copy it to your database location.
Rename the latest database backup file to 'StarReminder.dat’ and copy it to your database location.
Launch StarReminder and check your data.
 
Database path location
Depending upon StarReminder's version the database is located either:
in StarReminder’s installation folder (e.g. 'C:\StarReminder') or,
in '[Windows' Documents folder]\StarReminder' folder. 
 
Here you can read where you can locate your backup files:
http://www.starreminderapp.com/2/post/2011/10/are-my-data-safe.html