Sounds like your hard drive may be bricked... Do you have a good backup?
Try starting up holding command-r keys into your Recovery Volume.
The screen should give you these choices...
Restore from TM backup
Reinstall Mac OS X
Get help online
First run Disk Utility > Repair Disk, if you get errors run until no errors reported or reports "the disk cannot be fixed". Then, choose Reinstall OS X. This will be an install "in place" and shouldn't effect any of your own data or settings.
Computer got uber slow.
I started to worry.
Now computer won't start.
Tried to repair disk. Received error message above.
Any help would be greatly appreciated.
You can't have received an error message "Disk Utility can't repair this disk...disk, and restore your backuped-up file." since that is pure gobbledegook and isn't even good English.
What may have happened is that
(a) your hard drive has become so full that the operating system can't find any space in which to.... operate.
(b) as macjack says, it has crashed - possibly as a result of (a).
(c) you have been allowing Time Machine to back up to your internal hard drive instead of to a backup disk, which has caused (a) to happen.