Try restarting in Safe Mode, this will clear some caches. How you do this is when you hear the startup tone hold down the Shift Key until you see a progress bar appear. Let the machine fully boot and then restart normally. Also please be specific about EXACTLY what password you are referring to. Do you mean your account password, your iTunes password, etc... Please paint a clear picture for us, remember we're not there to see what you're doing.
I am having the same problem, starting today (12/15). Here's a more complete description of my problem.
About two weeks ago, I changed the email address associated with my Apple ID. The old address had been taken over by spammers, so it had to go. I followed the procedure in Manage My Apple ID, and everything seemed fine until today.
I am running Yosemite, 10.10.1 on an elderly Macbook Pro (2009)
I got a message saying I couldn't access iCloud and needed to log in in System Preferences. I tried logging in with my then correct password. After 3 tries I was locked out and told to use iForgot to reset my password. I used my recovery key and reset my password "successfully". My new password allows me to log into iCloud.com, iTunes on my Mac and on my iPhone 6, I am able to use my iCloud keychain on both devices, and I can log into Manage My Apple ID with the new password. I was also able to use the new password to log into iCloud on my iPhone. Access to iCloud drive from Pages appears to be working on my iPhone, but not on my Mac. I was also able to sign into the App Store on the Mac.
However, in System Preferences, I cannot log into iCloud and I cannot log into my iCloud mail account (both appear to use the same login). I get a message saying I have been blocked for security reasons and I need to reset my password. This is exactly the state I was in when I went and changed my password so it appears that the change didn't get communicated to system preferences. Without iCloud access, my apps that use iCloud for storage and/or syncing with iPhone apps are of limited usefulness. This may be key to the problem or at least a clue: System Preferences still thinks my Apple ID uses the old email address not the one it was changed to. The only way I know to change the address is through Manage My Apple ID
I tried rebooting by doing a full shutdown and restart, but it did not help. I also tried cursing at my Macbook but that did not help either.
I can use iCloud.com for mail and Documents since it recognizes my password. But this is at best a temporary work around. I'm off to check other sources for help. I'll report back when I know more.
I was able to fix my problem. I found a post on a different specific problem, but it was similar enough I tried the solution and it worked. It does require fiddling with a system file, but it's not really difficult.
Quit System Preferences, then
Find the file:
and change the file name, I simply added an X to make it MobileMeAccountsX.plist . (Note the irony of the legacy name.) Leaving the file but modifying its name makes OS X think it has to build a new file, but if this doesn't solve your problem or causes a new one, it's easy to restore the original name to the original file and be back to where you started.
Having done that, restart OS X. One of two things will happen:
If, like me, your Mac is already associated with your Apple ID, the system will rebuild the MobileMeAccounts.plist with the correct information, and you will then be able to go to iCloud in System Preferences and log into iCloud using your correct Apple ID. In my case, the iCloud control panel knew my correct email address, which I surmised it got from headquarters.
If this Mac has never been set up with the new version of iCloud, you will be asked to provide your Apple ID when the system restarts and the rest will be taken care of automatically.