Searched, and found this http://answers.microsoft.com/en-us/windows/forum/windows_10-win_cortana/cant-type-in-windows-10-search-bar/7dce8411-8671-4d3e-90d1-b9bdc0aa4734?auth=1. For some builds before 14371 this bug only happens after updating to the new build, which is easy to fix by the link above. But since b14371 it constantly appears, even when I just keep the computer running without shutting down.
Please fix this, it is really annoying when you have to restart your PC in the middle of your work just to be able to type in Start Menu and calculator again.