Yes, I'm in agreement with helltech, Your probably going to need ATLEAST a new graphics card and a PSU, however you may need a new case a CPU also.
I'll review your machine properly now.
EDIT1: upon review of you machine I've decided that your CPU will suffice, I believe you will want a new powersupply (450w minimum, 500~550w recommended; and from a brand name too[such as corsair, silverstone or OCZ]) and a 5770...
Your looking at a $200 upgrade here. Ill now go about getting the part pricing and information now.
EDIT2:
Power Supply 64.99 before rebate, 44.99 after.
Graphics Card 144.99 before rebate, 124.99 after, Usually I wouldn't pick powercolor(I haven't had any experience with them) however this card is OC'ed and also includes a Dirt2 Coupon. GREAT VALUE!!!
EDIT3: I also noticed that the 5770 I selected is the shorter version of the PCB so that should help with space, Im still unsure about your case however, You may still have to fork out another $40~$60 for a new one to fit all your gear in.