How to recover my harddrive if I can't see it in the disk utility
Sorry Rhubarb but the next step is to physically remove the hard drive from the iMac. If you are not comfortable then the best option is to go to an Apple Store or Authorized repair center and let them do it for you.

They might even be able to test the iMac, hard drive cable, and the hard drive for you. Best case the cable just crapped out. Worst case the drive is dead and recovery is not possible. There are dozens of things in between both of those but more can be said concretely once the drive has been removed and tested in another enclosure.