Well, I think the first thing to do is to determine if your pixel is dead or stuck.
A dead pixel, well, that's that. But a stuck pixel may be fixed by yourself if you're willing to put up with a series of seizure-inducing flashing screens. Granted, even the flashing screen fix may not work, but some people claim it actually does so at least you can give it a try if Apple won't let you take back the computer.
In regards to pixel policy and taking back the computer, I really think that depends on the Apple store and/or rep you talk to. I've heard personal accounts in this forum of people not allowed to exchange their computers for 1 dead/permanently stuck pixel, and others who can exchange even if just for a single dead pixel.
I bought the new 2009 iMacs, and after a week of having it, a dead pixel popped up. I had read about the pixel policy, but figured I would give it a try at exchanging it; the worst that can happen is they say no.
I went to the Apple store, told them I bought the iMac there just a week ago, and there was a dead pixel. They asked how many, and I said just one. They apologized to me that I got a bad quality Apple product and no questions asked (and no restocking fee) they gave me a new one. They didn't even check to see if the pixel was even dead. They just slapped a "dead on arrival" tag on the box, took it in back, and gave me a new one.
Now, as you've mentioned you didn't get it directly from Apple, I'm not sure how well that strategy would work. You could try to go to an Apple store and politely explain what happened, and take a chance that they'll be nice and let you bring it in for an exchange? Worst they can say is no.
If you can return it to the original online seller (is there at 14 day no questions asked return policy?) you could get the money back and just re-buy another one?
I hope it works out for you; my local Apple store was super nice, and I hope you can have similar luck!