iMac won't accept my password, which is definitely correct

Password for one Apple ID Account with Apple is associated to the account used to access your iCloud Account for that Apple ID Account

The Password for the Other ( Second ) Apple ID Account with Apple is associated to the account used to access your iCloud Account under the secondary Apple ID Account

How you are going to sort this out ?

Frankly, this is beyond me.

I have only ever used one Apple ID Account with Apple

I may suggest contracting Apple Directly

Start now and open an Apple Support Ticket as they are PAID  Apple Employees to deal will these types of issues . 

call 1 800 MyApple

Other location Call Centres 

 Contact Apple for support and service

Which password was it asking for? Apple Account (ex-Apple ID), computer password, eMail, etc

NineMuses wrote:

Computer password. I have only one account on it. Is something messed up in my keychain? Can't imagine why this keeps happening but it's very annoying, especially because I had to reset other things (new fingerprint, etc.) after I changed my password.

Normally the " Computer Password " is the very first Account used when the Computer was First Setup as New and out of the box.

Computer Password is, normally, not the same Password used to Log Into My Apple ID

The Computer Password, On the Computer, will become associated with your Apple User ID as well as the password used to Log into these Apple Support Community Forums

NineMuses wrote:

When my computer starts up, it asks me to login to my account. That is the password I'm talking about. Different from my Apple ID which I use to sign in here and from the one I use for iCloud (sadly, I'm one of those folks who had 2 Apple IDs and can't merge them). I want to be able to sign into my iMac and use it because I have a lot of work to do today, including placing a bid for more work which is due today and is already started on my iMac, and I can't access it because I keep getting the message that it is the wrong password (the "shake"). I don't want to try too many times and get locked out, like I did last time. I don't want to change it again in the Terminal and have to change all of the other things that will need redoing, if I can avoid it. Can anyone tell me what is wrong that it is doing this and how I can fix it?

Ah, the missing piece if the puzzle is revealed >> (sadly, I'm one of those folks who had 2 Apple IDs and can't merge them)

Will have to check this out as to what remedial actions maybe required to to put this right

PS the Terminal Command to reset the Computer Password would also create a New Keychain

You are welcome

If and only if you what ?

I can ask for help from those More Senior Contributors to myself to jump into your question

Just give me the word