I've used numerous different methods on various machines that worked, so I thought I'd document them here for you so you don't have to waste the time I did researching the issue. You click to try and input your password, but it quickly pops up then the password dialogue box disappears.
The message 'Need Password' is staring at you from the info bar at the bottom of the Outlook window.
You are using Office 365 and you turn on your PC and open Outlook but discover that Outlook requires a password.