Try changing to Digital Editions v1.7.2. ADE2.0 has lots of bugs, one of which is that it can't operate with Overdrive library books in conjuction with many Sony eReaders.
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editio ns.html
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172