Have you changed your apple ID? If you have, then your MacBook login is still using the old Apple ID and since you changed it to new one, neither the old nor the new passwords will work. Seriously.
I had the same problem but mine was even worse: my old apple ID was linked to the e-mail that is defunct.
Solution:
1. Log in to My Apple ID https://appleid.apple.com/account/manage
2. Click Edit next to your primary email address and change it back to the old one.
3. It will ask you to verify your new(old) email address. You can ignore this step (if the old email is defunct you have to ignore it anyway)
4. Log into your Macbook with the old password. If you don't remember the old password you should reset it in MyApple ID at this point. In that case you need to complete step 3 and if your email is defunct you may be screwed. Luckily I remembered my old pwd.
5. Once you log in go to Settings -> iCloud and sign out of your current (old) account (this will ask you a bunch of questions about deleting local copies on your Mac - it is safe to do so because you will relink these once you have a new account).
6. Under iCloud, create a new account using new email and update which apps you want to sync through iCloud
I highly recommend that you go to Settings -> Users&Groups and unlink your MacBook login password from the iCloud pasword so that this doesn't happen again .
I hope that helps!
