Your media is where you left it...
Should you be in the unfortunate position where you are no longer able to access your original library, or a backup of it, then see Recover your iTunes library from your iPod or iOS device for advice on how to set up your devices with a new library with the maximum preservation of data.
If you don't have any Apple devices then see HT2519 - Downloading past purchases from the App Store, iBookstore, and iTunes Store. Sign in to the iTunes Store with your Apple ID, click the Purchased link on the store home page, then Music > Not on this computer. Download links for your previous purchases will be there...
Thanks for the thorough response. I'll still need to get some help to accomplish the task - but having a good map will be very useful.
Indeed my desktop has died, but I do have a full backup on an external drive. Hopefully I can get my CD music back. However, I still can't get this machine to recognize me very well. I mean - even when I logged in to iStore as myself and asked for my purchased library - I only got back 1digital booklet that accompanied a record I'd recently purchased from my iPhone - not the songs.
So then I deauthorized this machine and DELETED the iTunes program, reinstalled iTunes with MY userid and the library STILL only displays the old owner's library. I don't get that. Sigh
Probably, I'll go see a genius in person this week
Thanks for being there