To start off I'll answer your questions: Yes the 8800 gt is enough to run Crysis, but not on your monitors native resolution or your monitors maximum resolution of 1920 x 1080. I found these parts based on a resolution of 1920 x 1080 if your monitor doesn't support that resolution (
samsung.com says it does), then please do tell, as I could recommend a much cheaper graphics card then.
Here is my suggestions (I'm including both $800 and $700 budget):
$800 budget:
CPU:I=
i7 2600k - $295
Mobo:
Gigabyte ga-p61-usb3-B3 - $80
Graphics card:
gtx 560 ti - $210
RAM:
Corsair 8 GB 1333mhz PC3-10666 - $36.24
PSU:
Corsair 500 watt - $50
HDD: (I really need to know what size your looking for before suggesting this one, in my opinion 120 gb is not enough space for a gaming pc. I speak from experience of having a 160 gb HDD). - somewhere around $50 for a 400 gb HDD right now (If you have an old hdd which you could use until the floods in Thailand clear up and they can start shipping out HDD's again that would be great).
OS:
Windows 7 Home premium 64 bit - $88
Grand Total = $810, I could have suggested a $10 cheaper coolmax 600 watt psu, but there are mixed reviews about the quality of that psu.
$700 budget:
Basically use the same components as above but get this for the processor and graphics card instead:
processor -
i5 2500k - $224.54 (from wal-mart they'll do free shipping to store or i'm guessing it'll be around 7 dollars to ship to home maybe less).
Graphics card -
gtx 550 ti - $131.38
With those two items you save $150 so 810 - 150 = $660 as your grand total (only thing would be the shipping from Wal-Mart if you choose to ship it to home).
As a Side Note: All these websites are reputable, and if they didn't seem like it, I did a background check to make sure they were, the sites I used to get the reviews: resellerratings.com , trustpilot.com, and some of them had reviews on google shopping.
Conclusion: The $810 build will get you more than what you're asking for, but I think it'll serve your needs for a long time to come especially since you'll be gaming at 1920 x 1080 resolution. The $660 build is more suited towards your needs, though I wouldn't exactly consider it a bare minimum gaming pc. Both the gtx 550 ti and the gtx 560 ti hit the 8800 gt out of the park, and they fit your budget.
Well do let me know what you think, and tell me how much storage you need for the hard drive.