Q: Mac mini only gets as far as the aurora screen.

Try starting in Safe Mode:

OS X: What is Safe Boot, Safe Mode

If successful then go to Disk Utility and repair the startup disk.

Next try booting from another bootable device if you have one.

See if you can get the optical drive to work by:

Apple Computers: Troubleshooting the slot-loading SuperDrive

Do you have an external USB DVD drive? You should be able to boot from that with an install disk inserted.

If you have another Mac you can try booting the Mini in Target Disk Mode and then looking at the disk in the Mini

How to use and troubleshoot FireWire target disk mode