Cannot find the Hard Drive on Disk Utility

I am using an iMac (mid 2010) the factory Operating System was Mac OS X 10.6.4 and updated to Mac OS X 10.9.1.

Following a "Flashinhg Question Mark" iMac was unable to boot.

Then installed OS X on an external HD and boot the iMac. http://support.apple.com/kb/ht5911

iMac is working with the external Mac OS but in the "System Preferenses>Startup Disk do not show the internal Hard Drive.

Following this issue the iMac fan is working fast and noisy.

I tried

1. SMC reset

2. PRAM reset

3. Safe Boot

4. Boot with the external USB Mac OS X

nothing helped me.

Thanks in advance for any guide.