Your copy of ADE, your old ereader, and all the books you download onto ADE are authorized with your Adobe ID.
You need to authorize the new eReader device with that ID as well.
Sounds as if you have been trying the right thing, but ...???
Is there any 'info' menu or similar on the device that will say what ID the device thinks it is authorized to?
Maybe the device authorization did not work quite right. Try ...
- With the device plugged in by USB,
- ctrl-shift-E to deauthorize the device (cmd-shift-E on Mac)
- restart ADE (maybe not necessary)
- menu/Help/Authorize Device (for ADE2.0/2.0.1), Library/Authorize Device (for older more relaible v1.7.2)
If that doesn't work, post back.