As far as the replacement computer goes, you're aware that it takes at least a product specialist level employee to issue that. For the upgraded parts I had to go higher than that person's authority. In my case since they were already giving me a $2100 iMac for free after having owned the previous computer three years and having a ton of money in parts and labour put into it, I too felt like that was enough on their part. I wanted to pay the $200 difference to get the upgraded video card, and that was where we ran into more issues. I had to call Apple Customer Support, ask for a Product Specialist, and then ask for her supervisor. They were very kind, and patched me through after asking me some brief questions about my case (case ID, is the problem still occurring, what is it that I am looking to resolve by phoning, etc), because if one of them was able to help me and had the authority to do it, they would be more than happy to have helped.
When I got through to this supervisor I explained my situation, the recurring artifacts making it impossible to do my work (I do wedding photography on the side), and that having been an issue for several months, I was happy to be receiving a new computer. But since my work involves graphically intense applications, a new computer with a basic onboard video card (which they were about to replace mine with) was of literally no value to me.
He then went and spoke to the customer relations committee, and on his return assured me that it wouldn't be any issue to give me the option to upgrade my computer for the replacement. The only catch, which you'll be happy about tclamp, is that it doesn't go through the Apple Store but through their offices directly!
( The nearest store for me is a good hour away too, and it was such a hassle to drive there, haul this heavy thing halfway across the largest mall in north america. )
They send you shipping labels, you put your imac in a box, and drop it with the prepaid labels off at any UPS. When they see the tracking sku in transit, they ship your new imac out to you! It's a pretty good system in my opinion.
Seeing that you've had to have your entire computer replaced so many times, you should mention how unsatisfied you are with the recurring issue at hand. I really do think that they'd be willing to upgrade you, and that if you go high enough they should be able to waive the upgrade price for the higher end processor. Just be polite with them, but firm. Make sure you tell them that you haven't been satisfied with the current platform, but appreciate all they've BEEN doing to try and accommodate you, and that you WOULD be satisfied if they were to upgrade you to a working [more powerful] system [for your troubles]. Three lemons in a row for one person is a statistical nightmare that they will want to remedy in my honest opinion.
