You disk or hardware is likely to be damaged. However in most cases you can still fix this temporarily. Be aware to check your hardware and disk permission settings by an expert.
Try First Aid 1–4…

This Indicates that your Mac can’t find or use the needed Mac system. Either your hard disk is severely damaged or other problems occured.
Try First Aid 1–4… and let your Mac check by an expert.

Your monitor or screen is connected properly and you still have no sound and a black screen? Then this looks like a power issue, a dead logic board battery, or bad RAM.

This can happen when the .Mac service undergoes service updates on Apple’s .Mac servers. Most of the time the Mac you try to sync is offline or has been interrupted during the sync process. Be careful! Cancel any syncing process and make backups of your Address Book, iCal calendars and Bookmarks!
Call the Mac Doctor for help.