I have a very similar system at home for my wife which came with the E4300 Core 2 Duo CPU 1.8Ghz, which has this same exact motherboard your system has. I ended up having to install a stronger power supply to fix similar issues because I had a video card installed that was drawing lots of power and made the system have BSODs with Vista.
Do you have a video card added that is running off the old original power supply? If so, I would swap power supply with a spare good supply if you have one of 400 watts or better in rating.
I have since upgraded my wifes system to the Core 2 Duo E6600 2.4Ghz with 4MB Cache when a CPU became available and its going strong still, however I upgraded her to Windows 7 and away from Vista when I bought a 3-license Win 7 family pack 2 years ago.
*If you have a video card added, you can remove this card and try running it on integrated video to see if the crashing stops as well, however the integrated video is not enough for most games if you play games, but if you can find that it is healthy without video card added then you know its the video card or power supply possibly.