No offense, but if all you are looking to play is WoW, then your current system is fine. It just needs an actual video card and a power supply upgrade. Get something good now for both of those so that when you save up enough cash for a good machine, it's just something you won't have to buy at that point. A good PSU can literally last through several upgrades.
The problem is seeing if your current computer has a PCIe slot. According to newegg for that machine and the pics I see, it has a PCIe 16x slot. This is good for you. If I was in your shoes I would do the following.
$150 Sapphire 5770 Vaporx 1GB card from Zipzoomfly. Linking does not seem to work with zipzoomfly so just search for 5770 and you'll find it.
$90 Corsair TX750W power supply
For $240, you can be playing WoW and some modern games with your current resolution and system. Both of these parts will still be good for a few more years to come. The power supply is a beast and will serve you well for many years and upgrades to come. The video card is great as well and if you ever upgrade your system, you can opt for a second one for SLI or you can sell it off for not that much less than what you would pay for it today.