Hi graywallis,
I did this recently - and seemed to be OK doing as follows:
Install the Reader Library software onto your new computer (I got the latest version off Sony's support website).
Then I went back to one of the on-line stores where I'd purchased a copy-protected eBook - most sites have your purchase history somewhere and you can re-download one of your previously bought eBooks. 'Open' the file and you will get the prompt to authorise your computer. For this you need your Adobe ID (usually your e-mail address) and password - it's really important that you use the same one as for your last computer or you won't be allowed to download the eBook again. And that's it!
Personally I just re-downloaded to my new computer all my eBooks from the sites I bought them (from the order history bit) - but I haven't bought all that many eBooks yet!
Hope this works for you!
