Will this all work together?

If you need a low profile graphics card, it also usually needs a low profile bracket on the end.
Visually, it looks to me that the card you linked to has a normal sized bracket which will be too tall.
In the package, I see no indication of an included low profile bracket.

Here is a slightly stronger card with the appropriate bracket for example:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...


The psu looks to be the appropriate power, but I am not at all certain about it's quality. But in a TFX size, and 400w, I don't see anything better.

http://www.ecrater.com/p/8951039/600w-power-supply-for-...

psu that is pretty long so i doubt that will be fit in your case correctly so take a look this one it has more wattage and cheaper and also 6570 is good for your system.

ok so do you think that pcu will fit and can i attach a psu outside of my sytem somehow if it doesnt fit? because im really not looking for a new tower and if its a stronger psu do you think it would have the right pins and connecters for the motherboard?

what do you mean by "pcu"?

Take the time to find out what the format of the psu in your case really is. Small cases will often have smaller than standard sized psu's. Measure the dimensions of your current unit. The psu you linked to is probably the correct size. It is a TFX standard which is much smaller than a ATX. While you are at it, see what it says on the data plate. Look for total wattage, and, more importantly, the maximum amperage on +12v. I really doubt that a standard ATX size will fit.

If you have an available 5 1/2 drive bay available, you can buy a 450w auxiliary psu that will power many graphics cards
http://www.amazon.com/FSP-Booster-Certified-Crossfire-P...

Most any psu made today will have the appropriate connectors that you will need.

i mean psu sorry was typing fast, and how many fps do you think i could get on a game like league of legends with very high settings on this gpu?

can someone do research on the psu i linked to were even if it fits like will it be of good quality?

It is entirely possible to build a pc without a case, leaving all of the parts out and just laying on a table or cardboard box. That is what I do to try out all of the parts on a new build before I put them in a case. To power on, you will need a way to start the pc if you do not have a pwr switch on your motherboard. A simple external switch is cheap. But if you have cats or kisd roaming in the room, it is not such a hot idea.

The psu you linked to is of unknown origin. It will probably do the job, but if you will eventually get a normal sized tower, it will not be very useful.

I suggest you consider getting a case up front. Good cases are not expensive.
You can buy an Antec 200 for $45.
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Quality psu's come from Antec, Corsair, Seasonic, XFX, and pc p&c to name a few.
You can get a Corsair 430W unit for $24 after rebate:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Also, the graphics card you linked to is not a real gaming card. It is certainly better than integrated graphics though.
Read this article:
http://www.tomshardware.com/reviews/fastest-graphics-ca...
Gaming cards worth getting start at $75 or so. If you do not limit yourself to low profile cards, you should be able to get more for your budget.

ok so i found this website that says everything about my computer and i dont understand about the psu it says like 240 but under it it says up to 270 or something but heres that link: http://bizsupport1.austin.hp.com/bizsupport/TechSupport...

and then i found this website and it tell me how much power i need to run things and a couple things on it i dont unerstand so if someone could do the blanks for me could you then tell me if i need to upgrade my psu or not anyway and if maybe i could still find an ok video card that i dont need to upgrade my psu with?

http://images10.newegg.com/BizIntell/tool/psucalc/index...

is the 6570 any good for gaming like would it work for games like battlefield 3 in like the lowest settings with 1280*768 res?

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

would that fit my pc?

ok so the way it looks id need a 300 watt psu to use a radeon 6670 is that correct? could someone help me find one of good quality and do i need the 20 pin adapter for it?

yes, thats ok but do not overclock.

ok thanks and will i need any special adapters or anyting or all i need is the psu and the card and thats it?

no need of any adapter directly works.

alright tyvm man

welcome! 

wait sorry i keep posting but on that sight it said 263 watt with everything if i unplugged my dvd drive so if i unplugged and stuff and i have a 270 watt psu would i even need to upgrade it?

no no, 270 is not enough for your enitre system get something like 400w.

what about 350 only good one i can find?

350w is also good way.