Hard disk icon has dissapeared from desktop

Simple. Load the Apple System start-up disc first while the computer is running. You should see its icon on on the screen. Then select restart from the Apple Menu on the top left of the screen. Hold down the C key as it reboots. You will now boot into the start-up disc. This method also applies to Disc Warrior and other tools. Alternately, with the computer already running, insert the Apple System start-up disc then go to System Preferences also under the Apple menu, Under the start-up disc icon, select your apple system icon and restart.
Third alternative. With the computer running insert Apple System start-up disc. Restart the computer. Before the chime, press and hold the option key, left-hand bottom side of the keyboard to the left of the Apple (Command) key. You will see your system HD icon and the screen as well as your Apple System disc. Click on the System Disc and that will boot the machine.

The power button is on the back of the LCD screen in the lower left hand corner. You should power down by clicking on the Apple Logo in the upper left hand front corner and choose "Shut Down". If your screen freezes, you can power off by pushing the power button and holding it.

all found in folders menu

Which icons are disappearing and reappearing? If you're talking about the Dock (The quick-launch and management area at the bottom of the screen by default), that may have been set to hide it's self, only showing when the mouse is at the very bottom of the screen.
Other icons that come and go are ones that represent volumes such as external hard drives, memory sticks, network places, CDs/DVDs. What icons are being problematic?
Hope that helped, please clarify problems if not!
Oh and by the way - iMac is just that particular type of computer. The Operating System is known as Mac OS. Knowing this will make getting help easier in the future :)

As the hard disk appears to be showing up when you boot up using the install disc, I would suspect that the system is somewhat corrupted. You could reinstall the system again and if you are happy starting from scratch and wiping the hard drive select this option failing that and there is some data on the imac you could install using the preserve user data. A fresh install should sort out any problems. Hope this helps.

Your new hard drive isn't "mounted" yet.
Launch your OS disc and run the disk utilities application from the desktop menu . Once in the application, you can choose to mount the new disc and name it and format it for use on your computer and then you can install the OS on your new disk.

You have accidentally enabled "Universal Access"
Open System Preferences from either the dock or the pull down menu under the Apple in the upper left hand corner of your screen.

In System Preferences the 4th line down should have icons for "System" one of those icons (usually the right most) will be a blue circle with a person in it. This is "Universal Access"

Open Universal access and turn voice over and zoom off.

checked that the column of macintosh HD icon is ticked in finder
I recommend that you trash the file Users > <yourname> > Library > Preferences > com.apple.finder.plist


Regards
Samson Ved

To add the hard disk icon back onto your desktop, first click the "Finder" button in the dock. It is the dark and light smily face icon at the end of the dock.

Next, click the "Finder" menu item at the top of the screen and then "Preferences". In the "Finder Preferences" window that opens, click the "General" button. From there you can select what system items appear on your desktop. You can click "Hard disks" to re-add the hard disk icon.

This sounds like the HDD hard died. Sometimes you can hit "option" at the startup to see if the HDD is corrupt. If you see a file with a questionmark in it, then you need to reinstall the OS, BUT before doing this, restart it and hold "apple T" it make the HDD and the computer a giant external hardrive. Just get a firewire cable and backup the hard drive onto another system before reinstalling.

If you see a disk icon come up, there is definate directory problems as it still recognises that it has a hard drive. Disc warrior might fix it.