Da CNet:
The likely cause is a corrupt system file which can be cured by booting the mini from the OS X installation disk, or the Recovery Disk that came with the mini, and running an Archive and Install of the system. Prior to doing that, and after you have booted the machine from an external disk, run the disk utility that you will find on the OS X installation disk. If all is well, proceed with the Archive and Install.
Archive and Install will preserve all your data while replacing the system.
Se a unidade de disco interna não funcionar, você pode tentar inicializar a partir de uma externa.