I realize I'm late with this post, but in the interest it may help someone;
As lightly touched upon, but not all the way, it is the OVERHEATING of the Nvidia GPU, (Graphics Processing Unit. Or graphics chipset ), and the subsequent partial melting of the solder connections, of the GPU in the BGA surface mount.
HP didn't incorporate sufficient cooling for the GPU, and just barely enough for the Processor.
The plates on the Cooling Tube are TOO small, for one.
The cooling system of the Pavilion dv9000 series of Notebook PC's, is the Fan Assembly, Heatsink, Cooling Tube, and the metal plates which are attached to the Cooling Tube.
There is a small metal plate which sits on top of the GPU. This plate is at one end of the Cooling Tube. Coming up the Cooling Tube a little further, is another small metal plate. This one a little larger than the one on the GPU, and sits on the top of the Processor.
One plate absorbs heat from the GPU, and the other plate absorbs heat from the CPU. (Processor)
Heat is then absorbed by the Cooling Tube.
The Cooling Tube is a slightly flattened copper tube, which is filled with Nitrogen, and sealed on both ends.
Heat is then transferred along the Cooling Tube, until it reaches the Heatsink at the other end.
Basic construction of the Heatsink is a plate of metal with Tall, thin fins protruding from it.
The Tall, thin fins absorb the heat, and radiate it away.
Air from the Fan Assembly helps to dissipate the heat. (Helps to carry the heat away from the fins)
The Processor, and the GPU are the two hardware components inside a computer, that give off the most heat.
Due to the plate of metal on the GPU is too small, the GPU overheats. This leads to partial melting of the solder connections, of the GPU to the motherboard. That leads to the computer not turning on, or bad graphics shown on the internal monitor. (And external monitor if attached)
The mounting of the GPU to the motherboard is done via a BGA surface mount.
Ball Grid Array.
To explain the BGA surface mount, allow me to use an older Intel Pentium 4 processor, that uses a Socket 478 processor socket.
The processor has contact pins on the bottom. (478 of 'em) The processor socket has matching socket holes. (478)
With a BGA surface mount, Solder Balls take the place of the contact pins.
Copper Pads on the motherboard take the place of the socket holes, and using a socket.
The graphics chipset (GPU) is set into place, with the Solder Balls lining up with the matching Copper Pads.
Heat is then applied at a specific temperature, and length of time.
The Solder Balls melt, which solders the graphics chipset to the Copper Pads.
(To the motherboard)
Constant overheating will partially melt those solder connections, and cause a poor connection.
(GPU to motherboard)
Non-professional method is to try using a form of heat, such as a propane torch, or hot air gun, with a metal heatsink made of tin surrounding the graphics chipset, and remelting the solder connections.
A very 'Iffy' repair. May work for a few days, weeks, months, or years.
Professional method is to use a BGA Rework machine.
Price? Can you say O-U-C-H?