It's not so much the quantity of RAM, it has more to do with the TYPE of RAM and the memory bus bandwidth.

Since you made the unfortunate mistake of buying an HP computer, odds are the video card you got has GDDR2 RAM with a 64-bit memory bus as a way to cut costs. With advertising, what's NOT said is often even MORE important than what IS said. In this case, they make absolutely no mention of what type of RAM the video card has, the memory bus size, or even the GPU and memory clock speeds. They spend all their time focusing in on how it has 512MB of dedicated video memory. You can bet a shiny nickel that if it were a higher end card like the one on that NewEgg link, they would be falling over themselves trying to extol the virtues and general greatness of the card by rattling off all kinds of statistics about it. You notice how they make a point of mentioning you have DDR3 RAM a little earlier, for example.

That being said, your computer probably isn't quite up to a card like that unless you replace the power supply. If you check the specifications on NewEgg, they say it needs at least a 500W power supply -- you probably have a 350-400W, and it'll be a cheap POS that's likely to burst into flames if you run it too close to capacity -- with two (2) 6-pin PCI-E AUX power connectors. Odds are your current power supply has none or maybe one.

So, you'd need to factor in probably at least an extra $100 or so to get a new power supply, and personally I'd go with an 80+ unit. Basically these are power supplies that are guaranteed to be at least 80% efficient in their power conversion. If you remember your high school physics, the final form of all energy is heat, so less efficient power supplies use the same amount of energy, but more of it just ends up being wasted as heat that has to be pumped out of your computer's case, and odds are HP skimped on the number of case fans. But more than that, you get more bang for your utility bill buck with 80+ power supplies. At least 80% of every kWh you draw using your computer, will go to making your computer do something, not heating up the place. There are some that are more than 80+, and you can get those if you want. There will never be a 100% efficient power supply, but 80-85% efficient is pretty good.