The old userid and password you got form the library should work on the tablet as well.
You say ON ATTEMPT TO DOWNLOAD TO A TABLET I CANNOT BECAUSE I HAD TO ENTER A PASSWORD WHICH I GOT FROM ADOBE.
Are you sure it really insisted on a new one, and would not have accepted your old one.
Try deauthorizing that new one you got from Adobe, and using the old userid/password instead.
Some people have had issues with OMS registration.
Try installing the Bluefire ereader app as well, and registering that with your old userid/password.
If that works, you may find Blueire adequate for your needs, or you may even find that registering Bluefire causes OMS to work correctly (as the registration really belongs to the tablet, not to the app)