GPU failure, can it be saved?

I have a mid 2010 iMac 21.5, EMC 2389. Forgive me, I don't remember the exact specs but I'm fairly certain it was the base model. I can't check since I'm experiencing a failure which I assume is the onboard graphics. Whenever I start the computer, it works for a few minutes and then I get either a checker pattern all over the screen or random lines. In either case, I am unable to click on anything on my display. From what I have read, my computer has a built in onboard graphics chipset. Given what it would take to replace this, I going to say it's pretty much unfixable. I understand (I could be wrong) that my computer also had an optional add on GPU card available when new. Would it be possible, if I could get my hands on one, to add this GPU to my computer and regain functionality? If this is possible, would the computer boot up using the new card or would I have to install an additional driver. I ask this since it might be impossible to install a driver with the old chipset acting up like it is. If anyone has any thoughts on this, please let me know.

Thank you,

Don

Ok, I looked up my serial number. Here is the URL: iMac "Core i3" 3.06 21.5-Inch (Mid-2010)