Ok. Lets say somebody downloaded some MP3s onto my computer from LimeWire. How is it possible for the RIAA or anybody else to track the files to me if my name is not on the internet account?

First, the files don't come from LimeWire (they come from other users through LW or whatever client they use.

I'd guess the name on the account would be liable, but that would be expensive to find out. Google will help you more--there's too much to be covered here.
see http://www.philly.com/mld/inquirer/b...6763845.htm?1c , for starters