Which Enter key?
OS? Version of InDesign?
Did you check the paragraph after the break for a Keep Option that requires it to start someplace specific?
Regular ENTER key (not numeric pad)
If I press ENTER after any character in those 2 lines of the header, it goes to the next page. 3rd line, works fine. Previous chapter last line, also good.
Does toggling the Numlock key change things?
Did you check for the Keep options?
Keep Options were set to next page for some reason.