There are bugs on ADE 2.0 that mean the Sony PRS-350 will not work with library books on ADE2.0.
May well be the same with PRS-650.
If so, replace ADE2.0 with the more reliable v1.7.2.
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