Unable to install the operating system

I have a 24" iMac Core2 Duo 3.06 (E8435) Early 2008 iMac 8,1 EMC#2211 System

I was given this computer and when I initially powered it up I was able to go online and everything seemed to work just fine. Then it stopped recognizing the operating system and when it was turned on it would just show the folder with the question mark flashing.

Wouldn't let me go into startup manager, diagnostic hardware test, safe boot safe mode,single user mode,verbose mode or recovery mode.

I got a new Apple OS-X Leopard install discs and tried to reinstall the operating system. It let me do the diagnostic test. I did the long one and it said everything is fine. I tried to re-install the OS and I got as far as the screen where it asks where I want to reinstall the OS to and there is nothing showing except the disc that I just put into it and the DVD drive. There is no icon showing the hard drive. That's where I'm at. I tried everything on the install disc but it doesn't show the hard drive.

Any suggestions?

I was thinking of replacing the hard drive but I thought I should check with the pros first.

This is just a hobby. But, I really want to fix it because it worked when I got it. I'm a PC/Android guy. This is my first Apple product. Any help would be greatly appreciated. Thank you.