Should be no problem a quality 450 watt would run that all day long. At least thats what Nvidias website says. I have a 550 running a 2.6ghz core 2 with 3 400 gig HDDs, SB audigy, Radeon 1950XT, ATI TV card, 4 gigs of ram never had any issues.
It all falls on the configuration/quality of this 680W PSU. Just like megapixels in digital cameras, a watt rating doesn't mean everything in power supplies. You've selected an 8800GTS which is going to need a minimum of 28 ampson the 12V. You SHOULD be fine but again it all depends. Check the specs for the PSU to make sure.
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