IMac 27" frozen screen

Question

just can not identify in what situations, but when my Mac has a frozen screen, I have no other alternative but to push the off button. The most ironic thing is that, clearly the internet connection keeps. I know this because I'm usually listening to online radio. When it occurs, I can not change my dashboard and also can not switch to another application because I can not use the keyboard and the mouse click does not work.
I am currently using Mac OS X Yosemite, but the problem has persisted for several other versions of the system.
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Answer 1

I have exactly the same problem with a my 27" iMac of exactly the same vintage and configuration. It freezes this way anywhere between once a day and once a week.
I also see an additional variation of this crash, where when I wake up the machine from sleep, the backlight comes on, but no image is drawn. It glows gray. In the form of the crash that Helton reports, the cursor moves with the mouse, but nothing responds to clicks. I've also seen where streaming (and I believe locally stored iTunes) continue) to play. I am not sure whether the machine remains visible on the network.
I have never used any anti-virus on this machine. In a desperate attempt to isolate the problem I have done the following:
Fresh clean install of Mavericks onto a new, external Firewire 800 drive
After the install, I only re-installed the apps I use frequently: iTunes, Aperture, Chrome, Adobe Flash and Microsoft Remote Desktop, HP printer driver, TextWrangler. That's it.
Replaced 3rd-party memory I had installed with the original factory installed 2x 2GB DIMMs
Blown out the bottom vents and the circular vent in back with canned air
Unplugged the external DVI monitor I was using
Done the usual setting resets via the startup
Ran the built-in memory checker at startup
Ran checks on the harddrives for errors, permission problems, etc...
Wiped the internal drive clean, and did a fresh install on that
The crashes still occur.
The system does not appear to be hotter than normal. I used to have a widget that monitors temps (but doesn't change fan speeds).
This system has the Seagate 1TB harddrive that was eligible for a recall, but I didn't do it. The drive has never reported any SMART errors.
Since you are still seeing crashes after updating to Yosemite, I'm not sure what to try next, myself. I've considered pulling it apart to make sure there is no dust in the fans. It doesn't seem to be overheating, but despite the sensors, there doesn't seem to be a way to record a regular temperature history to see what the temps were like at the moment of the freeze.
Of course, it's out of warranty. It's five years old, but it's plenty fast enough for me. The screen is still gorgeous. If it weren't for this, I'd use it for at least another two years. I was thinking of getting a MacMini to plug into it and use the iMac as a screen, but the new MacMinis are dual-core. It wouldn't be a nice leap in performance.