First HP are hard to upgrade, you need to check the front panel connector to see how it connects to the Mobo. Often HP use a special connector that's not compatible with a mother board upgrade. That can be worked around by tracing the wires up to the front panel, seeing what they connect to, HD light, power on led, power switch. Once you know exactly what they connect to you can re-seat the front panel connector pins in some standard 2 connector Mobo/front panel pins, most mom and pop computer shops glad to part with these for a couple of bucks.
If that sounds like some thing your not comfortable with then a new case, preferably with a front and back 120mm fan, those video cards run hot.
ECS motherboards which your HP has are kinda bad, I think of them as a bottom feeder Mobo. I don't know about that model, but the ECS I have had contact with I generally ripped out and replaced.
Here's an Asus Mobo that runs 85 to 99 depending on vendor;
http://www.newegg.com/Product/Product.a ... 6813131234, it's the Asus M3A 770 chipset. It has Pcie 2.0 which is what your Video card is designed for. It also accepts your current CPU, and provides forward compatibility with Phenom quad cores. The other asus boards that have PCIE run above 200, 230-250. Other manufactures support pcie 2.0 if your not an Asus fan.
Then I'd look at the wattage on the power supply, that video card is a heavy user of wattage, above 200 watt under load if I remember right, if it's a stock power supply it's probably gasping for life running that thing. Typically they have a 480 watt power supply, and usually not enough amp on the 12 volt rail to even run that video card. Reliable power supplies don't run cheap. Typically 100 to 150. A lot of the guys here run Corsair power supplies, here's a link to a 650 watt corsair
http://www.newegg.com/Product/Product.a ... 6817139005 Notice under specs, the 12 volt rail runs 58 amps, it runs 159, but tank out a stock power supply and you can lose your whole system. If I'm remembering right you need a minimum of 28 amps on the 12 volt rail.
Then that processor will throttle the card a little, you can try for an overclock on the cpu if you have good cpu cooling, probably not, what you probably have is the AMD approved FoxComm stock cpu cooler. Some of the guys ran tests on the 8800 line of cards, and 2.8 GHZ was the speed that the GT stopped being throttled. That's a big honkin card, 500 dollar range. To be safe I'd go 3 ghz on the cpu, or run the existing cpu and accept the throttling. If your going to go ahead and get Mobo and CPU I'd look into an intel board with a core 2 duo processor (more expensive, runs faster, easier to over clock)
Since you don't want to spend a fortune, I'd just get the M3A Mobo, the corsair power supply, and a good CPU cooler, then go into bios and use the AI Overclock, with a good processor and a little luck you'll hit 2.75 GHZ with the 10% overclock on that board. If it's not completely stable, come back here ask around a little, these guys are good at over clocking.