if you connect both computers at the same time, then you can simply transfer files by logging in using the system file sharing.

If you don't know how to do that, but you can get LimeWire running on both at the same time, then search for your own files and transfer them that way.

The least problem is to burn all the files to CD's, and transfer them that way.

There are lots of solutions--each depends on what system you are using to connect to the internet.