Possibly. It depends on what socket the motherboard uses and what the BIOS supports. I'd recommend looking to see what that computer was available with (old reviews help) and stick with those for processor upgrades. Depending on how much memory you have installed, that may speed up your computer quite a bit.
It can be done if the support is there in the motherboard. I've upgraded a Dell Latitude D531 (a laptop) from a single-core Sempron processor to a dual-core Turion 64 X2, and the difference was night and day.
Casey