ADE 2.0 refuses to work properly for library books in combination with most Sony eReaders.
Though the symptoms I saw (with PRS-350) are slightly different from yours:
for me the Sony does appear in ADE 2.0 and non-library books can be transferred as intended.
One possibility is some USB issue: does the Sony show up as a mounted device in your file manager?
If it doesn't show at all, the problem is before you get to ADE.
If it does show in file manager, one reason for failing to show in ADE is if Sony Reader for PC is not installed; but you say that is installed fine.
Does the Sony show up in Sony Reader?
Is this a new eReader that you have not yet managed to authorize with an Adobe ID at all?
If it is authorized, an alternative way of loading books onto it is to use your file manager (Windows Explorer, Mac Finder) to copy .epub files from the computer to the device.
You still neeed ADE to open the .acsm token files and download the real DRM .epub (or .pdf) files.
However, if the T1 is not yet authorized, you won't be able to read the books once copied.
What I suggest is that you install ADE v1.7.2 instead of (or as well as) v2.0.
That works faultlessly for me and my Sony even with library books.
There are lots of bugs in ADE2.0 (and 2.0.1). Try replacing ADE2.0 with the older but more reliable v1.7.2.
(You can have them both installed at once if you like.)
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
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
Some people have found ADE trying to upgrade automatically.
It appears (not 100% sure) that if you install ADE2.0 as a new install (not as an upgrade) that your 1.7.2 will continue to run.
Probably best to say no if 2.0.x installation asks if you want to migrate your library.