left side of iMac got dark

Have you run the hardware test that came with your machine?
Are you sure your power that you are getting it is reliable? A good UPS might help prevent issues in the future. If it does, then you might want to consult an electrician.

With respect to a brody and his 4 blue squares, this sounds like a problem with your display. I don't see a power mains issue causing a display getting dark on only one side. Apple Hardware Test might show something, but seeing as you said you got it "in the end of 2009", you will be getting close to the end of your 1 yr warranty. So, unless you have the protection plan, you should call Apple ASAP to get the issue documented, just in case your warranty runs out before the repairs happen.

Hi. I'm not sure if this would work, but you could try resetting the PRAM and NVRAM. It's worth a shot. Follow these instructions to do so:

Shut down the computer.

Locate the following keys on the keyboard: Command, Option, P, and R. You will need to hold these
keys down simultaneously in step 4.

Turn on the computer.

Press and hold the Command-Option-P-R keys. You must press this key combination before the gray screen appears.

Hold the keys down until the computer restarts and you hear the startup sound for the second time.
Release the keys.

or you could go here to read more about what you are doing: http://support.apple.com/kb/ht1379

there is a red exclamation point and a message next to it "failure".

The iMac can only be fixed by an authorized service technician when it comes to VRAM. And yes, that's not generally a power issue, but it could be prevented in the future by good clean power. Once your test says there is an issue, it is one Apple can usually believe.

The fact there was one once is believable enough. Just let them know that.

they will repair or replace my iMac without any cost, because I have the Apple Care Protection Plan?

As long as they determine you couldn't have caused the issue yourself. So just go in there calmly and explain the test revealed what it did that one time.

Backup your data first*:

http://www.macmaps.com/backup.html

- * Links to my pages may give me compensation.

Cool, didn't know if you had AppleCare or not. All of the other suggestions are good things to try, but I still think you have a bad display. Specifically a backlight problem.

If there was a video card problem, you would loose the image, not just part of it. Seeing as TechTools is indicating a problem with the video RAM also, I would take it to a service provider or contact Apple for warranty service.