Wow, lots of responses.
I just reread my OP and it is a little confusing. Here is a timeline:
Nov. 09 - Purchase of Refurb
about Jul. 10 IRC - 1st screen replacement
May 11 - 2nd screen replacement & HD replacement
Jul. 11 - 3rd screen showing issues / no power
Nowhere did I say that I was looking for a new MBP, although that would be nice. I'll be happy if they can fix it and not have to go back.
The reason I posted was to see if anyone could offer some first-hand advice directly to me (instead of me reading) about what I could justifiably hope/ask for in return for having to deal with so many major issues.
The computer is currently at the Apple store getting a full body scan. The genius said I should hear back by tomorrow what the diagnosis is.
+1 for you then. It got to the point where i was playing devils advocate because so many people said you deserved a brand new 2011 MBP. I wasn't trying to imply that you were trying to take advantage of anything.
If i was in your shoes i would ask for extended apple care for no charge considering how problematic the cpu has been.
You really need to show a continuing problem that is being fixed but is reoccurring. So if they can fix it check the screen. If it's bad send it right back. If it's good point out the reoccurring screen prob and the new prob and tell them how disappointed you've been. You'll probably need to talk to a manager or maybe even send a letter but it can be done.
If your computer can be fixed its very doubtful they'll give you a new one. But you might be able to score extended apple care if you play your cards right. Appeal to their sense of decency and don't demand anything or say you "deserve" anything and you'll get further IMO.
good luck.
EDIT: If i understand correctly the 3rd screen problem isn't really 'official' yet because you didn't report it and then the cpu failed. You'll have to want until it's returned, if it can be fixed, and point it out then and take it from there.