I agree, your current PC is no slouch. And there certainly is some improvement to be had by going toa newer, dual core CPU. But as noted you'll probably have to ditch your current memory to go to anything newer. There are a handful of mainboards out there that will support the Core 2 CPUs and have both DDR and DDR2 slots, but they tend to be cheap, not performance oriented, based on VIA or SIS chipsets and only have two memory slots of each type, which severely limits expandability.
Depending on what you are doing you have a few options.
1. Buy a new PC, as you mentioned. This will be the least satisfactory course I suspect.
2. If you're into gaming, put some of that money towards a new video card. Your current mainboard is PCI-E, so anything that you buy should be usable in your next system.
3. I recommend against buying a new CPU or memory for this mainboard, as socket 939 and DDR are both dead ends. I really wouldn't suggest spending money on anything that can't be used for the next system.
4. If you shop around you can probably move up a notch and get new components. You can get a 2GB DDR2-800 kit for $150 or so if you catch a special deal. Figure around $180 for a lower-end Core 2 Duo (E6300), $120 for a new mainboard (that won't be a super-duper "fatal1ty", but will be a reasonable board, and $150 for a lower-mid-range graphics card. So that's $600. This will be a little better than buying a complete system for $600, and while certainly faster than your current system it won't be that much faster.
If you wait for a few weeks Intel is supposed to cut prices in April, which means you can get a lot more CPU for that $180. If you are the overclocking sort then you could save $40-60 by going with an E4300 and overclocking the heck out of it. Or you could get the new mainboard, memory, and CPU now, and then wait a little while on the new video card. Once AMD/ATI releases their new line of video cards (also rumored to be April/May) you'll see prices drop a little due to competition in the DX10 space.
If I were in your shoes, I'd wait for the Intel price drop and then get the mainboard/memory/CPU, reusing your current video card. Then in a couple months get a new video card. That's the beauty of building your own, you can upgrade components as funds are available.