here is some link to the specs of the computer:
http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&docname=c01070924&dlc=en&lc=en&jumpid=reg_R1002_USEN#N292
http://www.newegg.com/Product/Product.aspx?Item=N82E16883107505
q6600, 3gb ram, GeForce 7350le, 2x320gb harddrive
motherboard-P965 with pciex16, pciex1, 2-pci
PSU-350watts 12v1-18A, 12v2-18A, max 300watts on 12v(double check this because the picture on newegg is really blurry)
It is obvious that the video card is holding you back. and I have two ideas for upgrades.
Idea #1
Msi 8600gt-79.99 with 25MIR
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127306
this will be a good jump from your current card. the reason why this card is because it doesn't require any additional power connections and your power supply will be able to run it.
Idea #2
OCZ 600w - 99.99 with 25MIR
http://www.newegg.com/Product/Product.aspx?Item=N82E16817341001
HD4850
http://www.newegg.com/Product/Productcompare.aspx?Submit=ENE&N=2010380048%204017%20106792627&bop=And&Order=PRICE&CompareItemList=N82E16814121253%2CN82E16814102747%2CN82E16814127359
they are the same except for the manufacturer and the msi one comes with witcher game for free.
this upgrade will cream idea #1, but will require you to replace the power supply and is more expensive. also i have concerns that these video card might not fit in the case. from the pictures it looks like it might hit the cage holding a hard drive and the front connections. I'm probably over blowing this, but check if the current video card was extended that it would fit under that cage before buy this.
if it was me I would do idea #2, but i can understand that some people don't like to mess around with hardware in computers which is why i gave idea #1.
changing the video card is very simple. unscrew the one screw and pull up on a tab next to the connector on the motherboard. then pull out the old one. pop in the new one and replace the screw. change the drivers.
the power supply is a little more difficult but not hard. disconnect all the power connectors to almost everything(motherboard, cd drives, hard drives, video card,...) and unscrew 4 screws on the back on the case. screw in the new psu and reconnect all the power connections.