Hello designsetc,
Thank you for posting on the HP Forums!
I understand your headphones connected will make your computer speakers louder. I will do my best to assist you!
Believe it or not, this is usually a hardware issue with the headphone jack. Rarely it is caused by a software discrepancy. Before this is confirmed, you would need to reinstall the operating system. It appears you have tried the common audio fixes for an issue like this.
Before you reinstall the operating system, you should backup your data. I can provide information on how to do this: Backing Up Your Files
Now, here is information on actually reinstalling the operating system: Overview of Recovering the OS or Reinstalling the Operating System
If this does not resolve the issue, I would contact HP phone support. You can utilize this website to learn how to contact HP appropriately, based on your region: Contact HP Worldwide
Please let me know if you have any other questions or concerns. Thanks again for posting on the HP Forums. Have a great day!
Mario