Q: How to install OS X El Capitan? App store gives me "To update this application, sign in to the account you used to purchase it" message and I forgot the password to that account

For Problems With Your Apple ID

1. Forgot iCloud Password
2. Forgot Apple ID
3. Apple ID - Apple Support
4. Manage your Apple ID primary, rescue, alternate, and notification email addresses - Apple Support
5. About your Apple ID email addresses - Apple Support
6. Get help with Apple ID

You can re-download the entire installer again, but not from the same account. So, you need to know what you have forgotten. We cannot help you. If you have no success then you can try calling Apple Support for help.

Contacting Apple Customer and Support Service

1. Apple Store Customer Service at 1-800-676-2775 or visit online Help for more information.
2. To contact product and tech support:  Contacting Apple for support and service including international calling numbers.
3. For Mac App Store: Apple - Support - Mac App Store.
4. For iTunes: Apple - Support - iTunes.