Stop-sign after boot and "Still waiting for root device"

Solution 1:

Apparently some important System Files got corrupted somehow. Although unable to boot, your data should still there.

You could retrieve your data by connecting your Mac Mini to another computer by FireWire. To do so just:

1. Connect the computers with the FireWire cable.
2. Boot your Mac Mini holding down T.
3. The Mac Mini's HD will be mounted as an external HD in the non-corrupted computer.
4. Find and save your valuable data.

Afterwards, making a Clean Install is the usual and fastest way of solving this issue.

I guess you can get this done for you in the Apple Store, though. Even more, if the machine stills under warranty.