T1 won't show up on ADE application. Install Sony Reader for PC and download your library ebooks using that application.
But if you prefer ADE over Sony Reader for PC, here's a work-around: If both your T1 and the ADE on PC are authorized with the same Adobe ID (the Sony ID doesn't matter), you can copy the .epub files in My Documents/My Digital Editions on your PC directly to the T1 via USB, and read them just fine.
Even if you don't remember entering Adobe ID on T1, try the above first anyway. Sometimes if your Reader for PC and ADE are on the same computer, and you synced T1 with Reader for PC, it seems to automatically link the Sony ID to the Adobe ID. If you can't read the epub book on T1, then try hard-resetting it, and go to Public Library on T1. You'll be asked to log in via Sony ID first, and then log in again with Adobe ID.
Hard-reset instruction:
http://www.kb.sony.com/selfservice/d...nalId=C1024494
(Remember to back up all the data on T1 first, because it will be back to clean factory-reset condition.)
I'm just sharing a work-around that worked for me. I prefer ADE over Sony Reader for PC as well, so I sometimes use this method (i.e. manually side-loading ADE-downloaded epubs to T1) and it works for me.