Can i use a GeForce 8600 in this system?

a 400W PSU should be fine

Does the "c" in the model # = compact = slimline = low-profile card?

I'm not sure what the "c" designation is for. But the tower is not much smaller than any other computer I've had in the past.

You may want to consider the 8600GTS - It runs quite a bit faster and does not use more more power or cost much more.

The 1950pro may be a little faster but uses more power and runs a bit warmer.

If you need a low profile 8600GT, you could get this:

http://www.gfe.com.hk/Product_Details.asp?id=135&class1...

Yes it should. Is that the stock PSU from HP that your referring to? If it is, you shouldn't have any issues. Like Zen said, 8600gts would be better for gaming, even a 2600xt AMD would be a tad better and you can get it cheaper here: $106 shipped no MIR's to worry about.
SAPPHIRE 100208L Radeon HD 2600XT 256MB 128-bit GDDR3 PCI Express x16 HDCP Ready CrossFire Supported Video Card - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Here's a link comparing some GPU's on UT3, just so you can see possible differences (at least on that game).
http://www.anandtech.com/video/showdoc.aspx?i=3128&p=4
8600gt = ~48 fps at 1280x1024 res
8600gts = ~55 fps
2600xt = ~58 fps
x1950pro = ~58 fps

Ok, I looked up 8600GTS, this one caught my eye http://www.newegg.com/Product/Product.aspx?Item=N82E16814127284, but where do i plug the fan in (i.e. psu, mb?)? Also i read some of the reviews and people were saying to use the 3 prong plug instead of 4 for a quieter running fan, so that confused me more. Again, thanks for the help.

On the back of the unit, there is a six pin power connection. Connect the six pin pci-express connection from your power supply to there.

The fan header is on the video card, so you just plug the 4 prong or 3 prong (both are attached) plug into it. It's powered by motherboard (there is a PCIe six pin slot on the edge that you should connect too, but curiously, it works just fine without it).

With that said, I used this card briefly before I RMAd the sucker and ponied up for the 8800, and let me tell you...that MSI 8600GTS is LOUD. It was so loud it overpowered all the other sounds in my case--I couldn't even hear the hard drive. It will improve a bit if you use the 3 prong plug (which slows down the fan), but the biggest fundamental flaw is that there is no onboard fan control. It's either on or off. I don't know why the Newegg reviews are so glowing. That card blew.

You need to plug in the power from the power supply on the six pin header. If not, you could destroy the card.

I'm not recommending that you leave it disconnected for the hell of it, I just mentioned it in passing. But it's not likely to "destroy" the card.

"Interestingly enough the nVIDIA drivers do not complain when the MSI NX8600GTS-T2D256E-OC extra power is not connected and it doesn't seem to affect 3D performance either. 3DMark05/06 scores and FEAR framerates were the same no matter if the six pin power cable was connected or not. Still, better be safe and plug it in."

http://www.pcstats.com/articleview.cfm?articleID=2105

If you cant tell by now, Im a complete nub at this stuff. Im gonna get the MSI 8600GTS. Is there a place on the mother board to plug it in or do I have to use the power cable that comes with it and plug them into the PSU. Also, if I plug it inot the psu connectors, do I just plug them into any available 3-pin connectors?

The 3 pin connectors would connect up to an available connection on the mobo. These are usually labeled a chasis fan or something like that. Check your mobo manual to see where you can plug it into. Part of the reason I spend a bit more on a good mobo, is that I'll have sufficient fan connections to plug into. These fan connections allow your mobo to control the fan speeds (if necessary) when the temperatures change (hot or cold).
The 6 pin power connector, that should be connected to the GPU, will take 2 4-pin power connectors (usually needed to power your DVD/CD/HD's) to make up a 6-pin connector. If your buying a retail version GPU, usually they have this converter cable (usually in a y format) in the box.

This is incorrect. The fan plugs right into the header on the board.

http://www.pcworld.idg.com.au/im.php/width/359/im/3515_...

It does not have a temperature sensor either, so it won't automatically control fan speed. You can't control it manually with Nvidia Control Panel either, though I didn't bother trying RivaTuner. It's either off or on at 100% unless you connect the 3-pin connector and then it runs at about 80% all the time.

That's a dual-slot card just so you know.