Shuttle make several types of machines, I wouldn't want to give you advise without knowing the specs (or model number at least) of you pc. The GeForce 7600 GT has a PCI Express interface which is probably going to be supported by your machine (but post your specs so we can make sure).
My main concern would be room to fit the card. So once we know the specific model, we can give you a reasonable assessment of the likely hood it will fit the smaller chassis (assuming it supports PCI E).
Well i did a bit more research and the news may not be good. http://blogs.zdnet.com/Bott/?p=176 Although it is a blog, I would definately contact Shuttle and check (in writing) the compatability of any intended graphics upgrade. Also consider your warranty.
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