whenever i open my macbook it asks me to "enter your password to continue using iCloud" and even when I enter the CORRECT password, it acts like it wrong and within 5 seconds is asking me to type it in again... what should i do?

El Capitan, Mac Pro 5.1. Before following your 3 step removals, I tried another approach described in this thread. iCloud was asking for my password for a few weeks with every start up. I opened all iCloud driven apps: iMessages, FaceTime, iCloud, anything in Preferences. Generally, my apple ID wasn't even showing up. I logged in (or out and back in if the user ID was there) and back in to them all then restarted. The pesky iCloud request is gone.

Does the iCloud pane in System Preferences show that you're signed in?

Please turn off two-step verification for your Apple ID, if applicable. Test.

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J. When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder. Select Library. Move the following to the Trash and restart.

Close all running apps. Put the following items in the trash:

1) In the ~/Library/ folder, put the Caches folder in the trash.

2) In the ~/Library/Application Support/ folder, put the folder iCloud in the trash.

3) In the ~/Library/Preferences/ folder, put the file MobileMeAccounts.plist in the trash.

Learned from Kurt Lang

This seems to have worked for now. I haven't had to re-enter the password yet.

I had exactly the same problem. I set up a new iMac to use my Apple ID/iCloud password, and although I could login successfully, within a few seconds the iCloud panel in System Preferences would pop-up and gave the me the 'Enter your password...' dialog. Then 5 seconds later the iCloud pane would get greyed-out and would ask me to re-enter my password.

When I set-up the account I enabled iCloud keychain, so I decided to try disabling it.

I found that immediately after entering my password into the iCloud dialog the iCloud settings panel was enabled for a few seconds, and I was able to disable (i.e. un-tick) keychain. iCloud hasn't asked me to login since.

So in my case the problem seems to be with keychain setup.

I am having the same issue. Just got a new macbook and ever since I keep getting asked for my apple ID and password to sign in on all my devices (macbook, iPhone, ipad2). none of these solutions seem to work for me. any other ideas???