Is this a Kobo dedicated ereader or tablet?
kobo touch ereader
Does the Kobo show up in your file manager (windows explorer, mac finder) as a mounted drive.
If not, there is something else wrong before it gets to the ADE (digital editions) level.
I think you need to make sure the kobo is turned on as well as plugged in.
Some devices will show 'charging' but will not connect if plugged in but not turned on.
Double check the usb cable and usb port are ok.
Backup any books from the Kobo and try a factory reset.
Comment from elsewhere ...
possible help with Kobo issues … I haven’t tried this
from post 23 in http://forums.adobe.com/thread/1124380?tstart=0 by Shirltaylor, Jul 26, 2013
Yes it was extremely frustrating process to read any library books after the upgrade to Adobe Digital Editions 2.0.
Eventually it turned out that the process must have you sign out of the Kobo device Account under settings on the Kobo Device.
What we did was to remove all library books from the Kobo device and from the Adobe Digital Edition
Next was to sign out of the Kobo Device as well as the Kobo Desktop on the PC as well as exiting from Adobe Digital Edition.
Next was to start up Kobo Desktop and sign in.
Next was to connect the Kobo device to the USB port.
This resulted in the Kobo device being upgraded and Sync'd to the Kobo Desktop. Wait until the Sync is complete
Disconnect the Kobo device from the USB port
Next was to restart Adobe Digital Edition and using CTRL-SHIFT-D to deauthorize the computer and select Erase Authorization.
Next was to go back to Adobe Digital Edition, Help and Authorize Computer
Next was to reconnect the Kobo device to the USB port
Next was to select the Kobo device in the Adobe Digial Edition and Authorize the device
Next was to get a library book in the Adobe Digital Edition and then add it to the Kobo Device
Everything seems to be working from then on.
Have fun reading again