Yes, Mac laptop screens have been having this problem for several years, and they never seem to fix it. They'll try to give you the run around if you want it fixed, but it's suppose to be covered, so just be persistent. But get it fixed soon. If it's only a week old and there's no evidence you've been banging it around, they can't blame it on "rough use." It's never "rough use" with Mac when this problem appears--it's faulty materials. But Apple loves to lay the blame on its consumers rather than take accountability for this. Think of it as their way of saying "Thank you" for buying their overpriced junk.
If this was me, I'd just take the thing back and get a PC netbook for a fraction of the cost. My HP netbook cost $300, weights about 2.5 pounds and survived a rough trip from Texas to Canada and back, (6 planes and a few hellish shuttle rides, without a ding or a burp. It's slow, for a PC (but probably still faster than a Mac) and the Windows 7 Basic on it could be better, but still beats a Mac.
For that same trip I got a Swiss Gear laptop bag. It was pricey but it too has held up exceptionally well. I use it now to tote my netbook or a laptop around town or to work, and it still look as new as the day I bought it. It's a shoulder bag, so not technically a hard case, but it's padded well enough. I use an additional Neoprene sleeve for my netbook because it's new and it has a cool design on the top I want to keep unblemished as long as I can.
My Toshiba laptop has been through hell and a Neoprene sleeve for it wouldn't help much at this point. Now, there a laptop that's had some really "rough use" over the past 3 years. And yet, no screen bruising. Scrapes and scratches everywhere on the outside and on the keyboard, yet everything still works just fine and best yet, the screen is still pristine, blemish-free and works perfectly. Best $700 I ever spent on a computer.
Seriously, get a PC next time.