It's possible the problem with the E8500 was caused by lack of power. The dell you mentioned comes with a 375W power supply. However, that doesn't really make sense since it has enough power for your current processor. Then again the power supply could be providing less than that now that it is 3 years old.
I would suggest saving your money and buying new....Your upgrade options are going to be pretty limited for that vintage as Enzo said. The money your going to spend would go a long way towards a new low cost machine that will in all likelihood outperform the older machine and provide a fresh upgrade path in the future.
That's a quad core server processor. It would be a large upgrade but not worth the price since you are not running a multi-socket server. Upgrade your motherboard and cpu in your current computer to something more modern for less than that.