@CRUISERF33
A failing fan is a hardware issue and updating the BIOS will not only not fix that, it risks trashing the PC in the process.
With a laptop, if you don't hear the fan, I suspect that it actually is NOT running -- and that is a serious issue as your PC will overheat almost immediately and shut down as a result.
That being the case, you need to get the fan replaced and such repairs can be very difficult and risky to perform, depending on how much stuff has to be removed in order to get to the fan to replace it.
For such repair estimates, you would need to contact an HP Repair or Service Center.
Since you live in the U.S., here is a link to the HP Service Repair Centers:
https://www.service-center-locator.com/hp-hewlett-packard/hp-hewlett-packard-service-center.htm
If that link does not provide useful information, use the main HP link:
https://support.hp.com/us-en/contact-hp?openCLC=true
Good Luck
I am a volunteer and I do not work for, nor represent, HP