First get a working password. Enter the Apple (iCloud) ID, and click Forgot Password. See if you can get a Rescue or Notification email option if necessary. Link to contact Apple Support at the end of the 2nd article.
Apple ID - Manage
Apple ID – Forgot Password *
Then follow the steps in this article to completely remove the second ID. Make sure you turn off Find My Phone before signing out of the old ID. Once signed out and Find My Phone is off, then sign in with the new ID, then turn Find My Phone back on.
What to do after you change your Apple ID or password - Apple Support. *.
Once you have done the above, see if you can access iCloud using the original Apple ID.
Have you tried restarting the computer? Are you running any anti - virus programs? Using a VPN?
Try setting up another admin user account to see if the same problem continues. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.
Isolating an issue by using another user account
If the problem is still there, try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer or by using the developer’s uninstall instructions. For each disable/delete, you will need to restart if you don't do them all at once.
Safe Mode - About.