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Although I now have a 300W PSU, I have been running a 6600GT and a xp3000 in my shuttle sn41g2 for over a year no probs with a 200W PSU ;)
So I would think you would be fine.
I have a shuttle SN41G2 with a athlon xp3000 2GBram and a 6600GT running on a 19" widescreen 14440x900 so this new 7800gs will be an exelent upgrade for me. Else i'd have to ditch the whole system and spend £800 on a new shuttle. By the looks of it this will give me nearly 100% performance...