When entering the administrator password while starting up the mac mini, the login screen keeps appearing again and again, prompting me for password.
This is a great troubleshooting question since there are about 5 things that come to mind that can cause this and you'll need some time and or another mac to did into the logs to determine the cause.
Before we start - does the password field shake left and right to indicate the password you typed was not accepted, or does it fade out smoothly to indicate the password was accepted and the user log in process is starting?
Next, you might find out your OS level to see if you have Lion or later and can use a recovery HD to boot and look at the logs. Alternatively if you know ssh and command line tools, you could try remotely logging into the mini.
Before you start down this road - try disabling the log in items by typing your password and then immediately hold shift down after pressing return. This is something quick to try before you reach out for support.
Here is where I'd start:
If you reach out to Apple or another technician, they should be able to walk you through the steps to make a new admin user in 30 minutes or less. Then you will know if it's your user or the system that has failed and you can start to proceed from restoring a backup or picking apart why your user has failed to let you log in.
If you've "forgotten" your login password, you can boot from the appropriate OS install disc and reset your password.
Once you've booted up from the Install disc, Choose
One caveat: If you've encrypted your data with FileVault, DON'T DO THIS.