If your desktop is the
HP Pavilion a1230n which I believe it maybe, then you still meet the requirements for the job. However your processor is almost as weak as the Pentium 4 and it is not dual-core. You have 2GB RAM according to your earlier post, in addition your most likely meet the requirements of 5GB free on your HDD.
The HDD is an acronym for Hard Disc Drive. You can find out how much storage you have left by clicking "Start" at the bottom left of your screen, and then select "My Computer" on the right-hand side of the menu which opened. Then you'll see a category "Hard Disk Drives" and if you right click on a local disk, usually C: and select "Proprieties", you'll find out your used and remaining space.
Since you're willing to purchase a new computer, you'll definitely be able to purchase a better performing computer than your current with your budget. When purchasing a computer, ensure it already has an operating system; either Microsoft Windows 7 or 8, don't bother with any other OS. In addition try and pick up an Intel system, not AMD, as I believe pre-built AMD systems maybe overpriced whilst not providing the best performance; then again the Intel systems maybe overpriced too, regardless you do get what you pay for with Intel. For your budget I'd aim for an Intel Core i5, sure an i3 would still meet your requirements by far, but for a pre-built system and $500 I would not expect an i3 and no GPU (I'm assuming no graphics card is provided). For your budget an Intel i3 or i5 is what I'd be looking at.
With all of that said, you don't have to worry much about the system requirements as those you have mentioned in the first post are "rock-bottom low-end" and any modern system you buy will easily meet them.
All the best.