Look in Task Manager, Processes tab. After OneNote "closes", is there a
ONENOTE.EXE process still listed? (If you see a "ONENOTEM.EXE" file, it is
a different program and not the one you're looking for).
Do any error messages pop up, from Dr. Watson or from the Microsoft Error
Reporting service?
Have you tried a "Repair" from Control Panel | Add/Remove programs?