IMac doesn’t start, all i see is colored lines and then checkered lines on a white background

I have iMac 2010 which is out of warranty. I recently came up to the computer and it was sleeping and was not waking up. I held the powered button for a while, so it turned off. Then I pressed it again. The iMac turned on, but I saw colored lines on the white background with apple logo and activity indicator spinning. It was spinning for a bit then the screen changed to checkered color lines and white background, and it froze that way. I turned on my TV that the iMac is connected to and all I see there is white screen. I tried cmd+Option+P+R and it did restart, but same thing happened. I also tried plugging out all the cables, including power. Waiting for few minutes and plugging them back in, but that didn't help. What else can i try? Do you think the monitor is dead or the video card? Hopefully not the hard drive. Here are the screen shots of what happens:

Update.
I am trying to do as little as possible, not to loose the data. I don't have much backed up.

I found the diagnostic CD and was able to run it. I ran the quick test and it found no issues. Now I am running the extended test. Would the extended test detect bad video card? I tried to start the iMac in Safe Mode with the same result. What are my choices, if it is the video card? To change it I would probably have to replace the whole motherboard, and Apple will charge I am sure over $300 if not more. Is there a way to boot from a flash drive to let's say Ubuntu and access the hard drive?

Here is the screen shot from that Diagnostic screen: