New authorization and on mutiple devices

Why is "Authorize Computer" not clickable?  I have new ebooks (epub format) and I can't read them.  Apparently my copy of Digital Editions was originally authorized under another email account.  I suppose I need to link accounts.  How can I do that without deleting my current installation?  If I do that then I probably lose access to my existing library, right?   Also, while I have downloaded by ebooks to my computer, I want to be able to read them on my tablet.  Do I have to go through this whole ordeal again for that device?