How to reinstall QuickTime player 10.4 with EI Capitan?

Combo updates may or may not include full applications. One may need the full OS 10.11.6 installer to be certain. (Combo updates just combine iterations after the initial release.)

More importantly, QuickTime probably doesn’t need reinstalling, as the issue is likely not with the application and its system components, but instead with preference files and/or other users account specific settings.

• Safe mode can help you to determine whether an issue is caused by software that loads as your Mac starts up. How to use safe mode on your Mac - Apple Support
• The issue could be related to the files or settings in your user account. How to test an issue in another user account on your Mac - Apple Support

Reinstall the last El Capitan Combo Update: https://support.apple.com/kb/dl1885?locale=en_US