I had a 2009 iMac (27'') that was not working correctly. I called Apple support then took the iMac to the local Apple store. After taking the iMac back to the Apple store a couple times and waiting a week, I get a call from the Apple store saying that it is no longer cost effective for them to try to fix my 2009 iMac and that they will be giving me a new iMac. My new computer is not a refurbished iMac but one of the newly released 27'' iMacs (which are currently on a 2-3 weeks backorder). I was also able to buy AppleCare on the new iMac (some companies don't allow warranties on replacement products).
By the way, it turns out I called Apple support on the last day of my AppleCare coverage.
And yes, I am a very happy customer! Thank you Apple (and the local Apple store)!