Is there a piece of hardware that I can buy that will allow me to use more than the two slots my machine provides for memory? If so will it run as fast on it?
There is no way to do that period.
If you have vista this might give you some performance gains using a USB memory stick:
I think no. The memory is connected to the CPU by the "Northbridge" of the chip set that supports the CPU:
There are some applications that use the video processor and associated memory to do complex computations. Also, there were in the 1990's some motherboard designs by Intel that attempted to be "modular". Outside of that, one would need to try an re-engineer the motherboard and the CPU Chipset.
I would imagine that even if it existed in the form you are looking for it'd have a hard time beating the piece of hardware called 'motherboard replacement' for price.
Replacing the motherboard also has the benefit that there aren't going to be any unexpected performance downsides to using a non-standard connection between the processor and whatever memory you manage to add.
Gigabyte makes various RAM disk offerings that allow you to add memory modules to your system. This is treated like a solid state drive in essence, so pointing a swap file to it for example would boost performance. It will not be treated as normal RAM to be sure, but it does let you add more, and it can certainly help.