Thanks to everyone that posted! This helps me out so much, and I didn't think that anyone would respond so quickly either.
Another reason Polycount is the best forum out there
The main question I need answered still though is what exactly do I need to copy over to my new comp?
I have copied the folder containing all my models, .ase files, textures and my .udk files. You guys mentioned something about the .upk files. which folder are they in?
I'm guessing it's something like C:>UDK>UDK-2010-09>something or other...
Thanks again everyone!