Greetings, wamest, and welcome to the Gnutella forums!

Sorry about your loss, but glad you got a new machine.

Whatever files you downloaded via Limewire are where you put them. There is no other place where downloads are stored for you, nor is there a list of what you downloaded. You will have to recover your files from your old computer (if you haven't buried it yet).

You could possibly move the old hard drive to the new computer or an external hard drive housing. I bought a used small external drive and used it to house my old, larger drive (and didn't have to move any of the files!).

If you have already recycled your old machine then, alas, your files are gone.