To make it work, you need the computer and the device authorized with the same AdobeID.
This must be an explict AdobeID, not an 'authorize computer without ID'.
Maybe you registered the old computer with your AdobeID, and the device from that?
And maybe with the new computer you have not yet registered your AdobeID?
Assuming you are on ADE2.0, check that with ctrl-shift-I to ADE (cmd-shift-I on Mac).
That will tell you the ID you are registered with.
If the new computer isn't registered with your ID,
- crtl-shift-D to ADE to remove any trash registration it may have
- restart ADE
- Register ADE with your AdobeID (ctrl-shift-U)