I have an Nvidia 8600 defective card, as many people do in their dv9000 series laptop. Updating the BIOS and the driver won’t work. Buying a cooler, and cleaning it out won’t work either. If your card is beyond an small fix(completely dead), you will need to have the motherboard completely reinstalled. After you get it installed you will need to add a thermal compound/shimmy to buffer the overheating from happening a 2nd time. There are videos all over youtube on how to do this. If your laptop isn’t totally dead yet, just over-heating, use the youtube trick+ the cooler and clean it out with compressed air.
If you get a case manager to work with you on it, he/she can give you a discounted price for a new motherboard and labor - around 300 bucks. Understandably, HP can’t service everyone, because the truth is, more and more people are coming forth with different chipsets complaining that they are defective as well from Nvidia. This is a Nvidia issue.