I'm in the same boat with the same computer. I've been investigating options for a while. I chatted/talked with Apple Support at some length today, and they told me that the Apple Store--which is the closest place to get service for me--won't give me any price quotes, as there may be more than one thing wrong with the computer, and they don't want to be accused of underestimating the cost. They suggested that I box up my computer, take it over there, and see what they had to say. They also told me that they'd only be able to put in an Apple SSD. I don't know if any of this is true, but I heard it from more than one person tonight. This seems like a crappy option to me.
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Has anyone taken advantage of this program? It seems like a good deal to me if it's as advertised. What would I do, put it in the original box w/original packing materials, ship it to them, let them fix it, then have them ship it back to me?