I have a new computer with VISTA. Have/had the "Basic" Limewire. I previously had Limewire on my old computer with lots of downloads. How to I transfer this information to the new one without starting over. Or can I ?????

As far as I am aware the only way for you to transfer the previously saved files would be for you to burn a CD or DVD of those songs you want to keep and tranfer them from one computer to the other like that.
You would also have to start again with Limewire by downloading the current version and start from there.