Q: Why can I not sign into iCloud or iTunes on my iMac?

Hello acarter5104,

Thanks for using Apple Support Communities.

If I understand your post correctly, you are unable to log in with your Apple ID in iCloud and iTunes services, however you can log in to the same services on your other devices on the network.  Since it's only with this specific iMac, I'd like you to do some isolation steps to find out if this is a system-wide or user based issue.  To start off with, I'd like you to start your computer in safe mode, and try to sign in to iTunes and iCloud.  You will notice some different behavior in safe mode, such as the screen loading in a series of lines, but that is expected.

Starting up in safe mode

Follow these steps to start up into safe mode.

1. Start or restart your Mac. 
2. Immediately after you hear the startup sound, press and hold the Shift key.
3. Release the Shift key when you see the Apple logo appear on the screen.

After the Apple logo appears, it might take longer than usual to reach the login screen or your desktop. This is because your Mac performs a directory check of your startup disk as part of safe mode.

To leave safe mode, restart your computer without pressing any keys during startup.

If you don't hear a startup chime after pressing the power key, see what to do if your Mac won't turn on.

If you're using FileVault

If your startup disk is encrypted with FileVault, you can still hold down the Shift key immediately after powering on your Mac to start up in safe mode. You might be prompted to log in twice as part of this process – first to unlock the startup disk, and a second time to log into the Finder. You can let go of the Shift key after you see the first login screen.

If you're still unable to sign in in safe mode, then I'd like you to create a test user on your Mac, and try to sign in when logged in to the user.

How to test with another user account

You can figure out if unexpected behavior is related to user file or setting by trying to reproduce the issue from another user account. This process includes creating a new user account, logging in to it, and testing for the issue.

Create a test user account

1. From the Apple menu, choose System Preferences.
2. Click the Users & Groups icon in the System Preferences window.
3. Click the lock icon, then enter an administrator name and password.
4. Click the Add button (+) below the list of users.
5. Choose a type of user from the New Account pop-up menu.
6. Give the user a full name, account name, and password.
7. Click OK.
8. Close the System Preferences window.

If there are documents from your original user account that you want to test with, place a copy of these items in the Shared folder in the Users folder. Press the Option key while dragging a file to this folder to create a copy.

Log in to the test user account

Log out of your current user account by choosing Log Out from the Apple menu, then log in to the new account you created. If you're prompted to sign in with your iCloud account or Apple ID when you log in, skip this step.

Please let us know what the outcome is, so we can further assist you.

Take care.