Q: Turning camera on on Mac computer

It should turn on automatically when you open FaceTime. You should see yourself in the open window. You can also try it out in Photo Booth.

If it's not working then try rebooting the computer and trying again.

No. I would take the computer in for service, then. Sounds like your camera may have failed.

(1) Because rebooting did not help, consider Apple's How to Troubleshoot iSight.

(Over time, Apple has changed the built-in camera's name on newer Macs from "iSight" to "FaceTime" and then to "FaceTime HD."  Regardless of the name of your Mac's built-in camera, the same info and troubleshooting applies.)

(2) If you are using OS X 10.9 also see:  iSight camera failure after OS X 10.9 Mavericks update

Jessobrien wrote: Did a reinstall of Maverick... Everything from the desktop "disappeared"...

If you did not erase your startup disk before you used OS X Recovery's "Recovery System" method to reinstall, you should not have lost anything.

Unless you mark the "Reopen windows when logging back in" check box in the Shutdown, Log Out,  or Restart dialog box before proceeding, it is normal that items open on the desktop are not automatically reopened when you see the new desktop.

If you store documents on the desktop instead of in your Documents folder, try a restart to see if the items reappear where you think they should be. You can also use Finder to manually look in your Finder > Go > Desktop folder to see if they might be visible there.  One other idea is to try a Spotlight search for a filename you remember to see if they might have been moved somewhere you can find them. 

If you cannot find them manually, repairing your disk is appropriate.

Jessobrien wrote:... We are attempting to repair some HD items issues thru Disk Utilities....

To repair your Mac OS X 10.9.2 startup disk, you should have restarted the Mac using ⌘-R to launch OS X Recovery and then select the Disk Utility in the Recovery System's "Mac OS X Utilities" window.  After any needed repairs are complete, you need to quit this Disk Utility and restart your Mac normally to return to your startup OS and desktop.

You can verify the disk to see if any repairs are needed.  As explained in Disk Utility 12.x: Repair a disk, Disk Utility will prompt you to take further action if the software cannot make needed repairs automatically.

Jessobrien wrote:... It says "there are an incorrect num of HD items. HD could not be repaired".  Does this mean we have a bad HD?

It means the file system is damaged and Disk Utility could not correct the problem.

If you were using the Disk Utility from your Mac's Finder > Go > Utility folder, use the OS X Recovery Disk Utility method explained above. Perhaps that Disk Utility can successfully make the needed repairs.

If you were already using the OS X Recovery Disk Utility method, contact Apple or your Apple Authorized Service Provider for help.

Jessobrien wrote: ... reinstalling Maverick seemed to fix the initial problem...

It doesn't seem that unusual for reinstall to fix it.  Happy you got it working.

Jessobrien wrote: ... Next step is to back up and cleanup the computer in case something like this happens again

Good plan.