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Within AdWords account the quality score is appearing as Great. The minimum bid is high enough and so is the max bid. Like I said before no one else is bidding on this term.
On another note, if you have a term that returns no organic results it seems to me that it would only take a couple of good links with the term in the anchor text to get that page to show up in the organic results. If I read correctly, you’re trying to promote a vanity domain which leads me to believe that there is a more prominent domain behind it. I would suggest using the influence of the main site to throw some links to the vanity site. You can bet that your competitors will be trying to rank organically for that term. ;)
Also, I don't think that raising your max CPC will have an instant effect, you may have to give it a little time to move.
Also, also, be sure that you are checking on the ad with the ad preview tool as this will give you a view of what the rest of the world sees.
Here's more information on "top placement" from the AdWords Help Center: