iMac Internal Hard Drive Not Visible, Won't Mount; Currently running off External Drive
It does sound like your hard drive has failed.

Have you tried booting up and using Apple Hardware Test? To do this hold the D key down while booting up. 

If AHT doesn't load, you can also trying running it from the internet by holding down the Option D keys while booting up.

Give this a try and let us know how you go.