I totally forgot about your shared files. duh
Well by default your downlds are saved here: C:\Documents and Settings\"your account name"\Shared
And if you open LW, go to menu bar, Tools>Options>Sharing & it will tell you the locations of the other shared folders. You can go to Library window & select these & press Explore button & folder will open up for you. So you can move however you'd prefer. Be that by burning to RW disk or networking the 2 computers, etc.

To add them as shared folders on the new computer, see How to Share Folders (click on link)