In my experience with this, its because a previous account that you used is still being remembered by Office and it conflicts with your Park account. Its also possible that Office simply needs to be reinstalled or both.
Step 1: Backup your system either by using Time Machine or backing up important files onto a flash drive or external drive or using iCloud or any other cloud storage service.
Why? Because the fixes we will use have a very small chance of breaking apps or files. This is true when trying to fix anything and its always a good idea to backup unless you don't care whats stored on your device.
Step 2: Open "Keychain Access". You can find this by pressing Space + Command.
This will pull up Spotlight Search which you can then search for Keychain Access. Should look like this and make sure that under "Category" you have clicked "All items" and under Keychains you clicked "login" looks like the screen shot.
Step 3: Once opened, you will need to do a search in the top right corner for "Office". This will give you the result "Microsoft Office Credentials", delete it by right clicking and selecting delete "Microsoft Office Credentials".
Step 4: Close Keychain Access or use the keyboard shortcut Command + Q
Now fire up Microsoft Word and sign in using your IDfirstname.lastname@example.org along with the same Park password.
If this doesnt work, remove office and reinstall it but make sure you have a download of office with you before doing this. You can get this by going to portal.office365.com, sign in and click install office in the top right corner next to your apps for online.
The link here will show you how to delete the apps for office as well as some hidden items. Again, only do this if the first solution didn't work. May need to repeat first solution after doing this one. Its complicated.