If you have iTunes, you can upload your MP3s from a shared folder on your other computer if you have a LAN network, bypassing the whole iPod transaction.
Make sure that "Copy files to iTunes Music folder when adding to library" is checked (under Preferences-->Advanced). Then go to File-->Add Folder To Library, and select the folder that contains all of your MP3s (subfolders will be imported as well). You will lose your playlists, but they are fairly easy to set up again. You'll have to format your iPod to your new computer anyway.
Alternatively, all of the MP3s are shown in disk mode on the iPod under hidden folders. Open up any old folder on your computer, go to Tools-->Folder Options (under WinXP), click the "View" tab and ensure that "show hidden files and folders" is selected. Then open up your iPod under My Computer, and browse through the hidden folders (transparent folders) till you find all your MP3s. The filenames will be truncated but that doesn't matter once you import them back into iTunes .. all other information is retained.
