Paying more than double is not going to provide "ten times" the performance of the athlon, don't listen to that guy.
It amazes me when people will talk about things as if they knew what they were talking about when they have no clue. I also meant to say throw in $100 to make the total $500 for your purchase. If you had $1,000, well you could completely destroy that $400 HP system.
Anyone who has a $500 budget (not including monitor, OS, or peripherals since I am talking about an upgrade) should check out this thread at Toms Hardware.
Building with a $500 budget
Compared to that HP system with on-board graphics, to a C2D 2.6ghz with a motherboard and 4gb of memory that will allow you to over clock your system to 3.0 without even trying, on a stock heat sink no less. All paired with a 512mb Radeon 4850 and I would say that I severely underestimated the performance gain, especially when you consider you can't even start most modern games with almost every integrated video solution available.
On top of all this you get an Antec 300 case which is badass and will hold massive cards like the GTX 260 (barely), and you get 120 more gb of storage, and a quality power supply that will last you for years without problems, which is probably the most important part in your entire system. It doesn't matter how much it costs if it doesn't run or suddenly turns off because you have a cheap power supply.
Here is another guide using $500, but they went with 2gb of ram to be able to use a Radeon 4870. It plays Crysis at 40 fps! If you paired a 4870 with the Athlon 4850e at non hi def resolutions, it would be bottle necked, so you would need to upgrade both the card and the processor.
If you need instructions on how to build your computer, there are a ton of guides online, just search google. It is so easy as long as you find a good guide to tell you the precautions you should take and walks you through each step.
For benchmarks on all the equipment I talked about, you can go to Anandtech or Tomshardware. They are immensely useful due to the daily deals on most websites selling this hardware. One day you might get $40 off of a combo and you need to quick see how well the part bench marked. And yeah, the combo deals. Newegg (for people in the states) has tons of combo deals on all kinds of parts. If you look out for those, you can save $50-100 on most full system builds.