iCloud/iTunes sign-in issue

Been out of town for a week and yesterday I noticed that the Macbook was asking for the iCloud password upon startup. It wouldn't accept the known password so I just ignored it. However, this morning the same thing happened. I could sign into my Apple account online with the same password so I ended up resetting it for the Apple account/iCloud account and restarted the computer. Same thing on boot up: asks for iCloud password.

Yesterday, when all this was initially raising its head, I downloaded an iTunes update, thinking that would solve the problem. But if I open iTunes it rejects my password and I then get stuck in a password rest loop across this Macbook and my iPad. It's driving me insane!

Running Yosemite on a mid-2010 Macbook Pro.