Unable to boot my iMac

Problem first started with the flashing folder w/question mark. I was on the phone with Apple support and they walked me through all steps, problem could not be solved. (command + R, command + R + P). At the time, I was unable to connect to a different network. I did find an ethernet cable and tried all the steps but no luck.

I took the computer with me to work to plug into a different network, via wi-fi, and was able to get to the disk utility but when I ran it, it said the HD could not be verified and could not be repaired. I did not attempt to use the ethernet cable at work.

I tried again at home and this time I got the apple logo followed by the "no" symbol. The nearest Apple store is 300 miles away. The nearest Apple certified computer repair is an hour drive away but charges $75 for the diagnostic and after that $75 per hour.

Is my hard drive fried? This is beginning to sound like it will not be an easy fix or an inexpensive one.