I would loved to do this just for the fun even if I would have to link up multiple computers up to each other just to get the processing power enough to light it up. Is this possible or am I not understanding something?
If this is possible how would I go about doing this?
Yes, it is possible but very very uneconomic.
Computing power is not a form of energy, is a way to consume electric power transforming it in heat (which is a disordered form of energy).
A bulb is just another machine that transforms ordered energy (electric power) in disordered energy (light and heat). Not so different from your CPU.
You can get ordered energy back from disordered energy (with a thermal power plant) but only wasting most of it:
http://en.wikipedia.org/wiki/Entropy