Here is a suggestion for you, and exactly what I did. I needed to update the PC I use for downloading, burning CD/DVD, streaming music and video around the network, managing files etc... And this was my solution:
An i3 540 CPU, Asus middle of the range motherboard, 4GB DDR3 ram, Arctic Freezer 7 Pro cooler, 600W Coolermaster PSU. All that cost under £200 and is amazingly fast for the money.
The i3 CPU is more powerful than its price tag might suggest, and they are actually dual core CPUs with hyperthreading, so the OS sees then as 4 cores, and my 540 runs at 3.06GHz stock speed so is nice and fast out of the box. It also has speedstep which reduces the CPU clock speed to around 1GHz when idling which reducing power consumption and keeps the CPU cool. Mine idles around 24 - 28 Deg C, and even under load never goes over 40 Deg C. The i3 also has built in Intel graphics, so with a compatible motherboard you don't even need a separate graphics card if you are not gaming, and the Asus board I'm using even has dual VGA and DVI outputs so I can run a dual display setup from it. Such a setup is still a lot faster than your current AMD X2 system and would be exactly what you need. And its still good for a spot of gaming if you wanted by added a dedicated PCI-E graphics card if you wished. Obviously an i3 won't deliver the power current game releases need to run on high settings, but its great otherwise and I think ideal for your needs.