1) Ensure that none of the hardware components are overclocked.
I don't know how to overclock nor to I care to so they should still be on standard settings.
2) Ensure that the machine is adequately cooled.
A few weeks ago I got help to tear the laptop apart and replaced the thermal paste. It is sitting on a nice open table, the fan setting is always on, and I have a cooling pad for it. Since replacing the paste is has never passed 80c and is running 10 degrees cooler than it previously had so heat should no longer be the issue unless there was some kind of thermal damage, but none of the components were physically ruined when we took it apart.
3) Update all hardware-related drivers
According to Slimdrivers almost everything is up to date. Anything that it doesn't have listed as up to date I believe I had already tried but I could always check those again. It is possible there is a driver issue or conflict, but I don't know how to test for that.
4) Update the motherboard BIOS according to the manufacturer's instructions.
I did this early on, of course HP is not very good in providing updates so there was only one.
5) Rarely, bugs in the OS may cause "false positive" 0x124
Ok not sure how to check for that, but windows has been re-installed, plus this is a new drive now and there problem is still there.
6) Attempt to (stress) test those hardware components
Torture tested the CPU and stress tested the RAM, both passed fine going for hours without a problem. Have run chdsk both the original and the new drive and found no issues. I don't think I had a program to test the GPU.
7) As the last of the non-invasive troubleshooting steps, perform a "vanilla" reinstallation of Windows
Done this, in fact that is what I am running for Windows 7.
8) Clean and carefully remove any dust from the inside of the machine. Reseat all connectors and memory modules. Use a can of compressed air to clean out the RAM DIMM sockets as much as possible.
Did all of that when I replaced the thermal paste as a dv6 requires a complete tear down.
9) If all else fails, start removing items of hardware one-by-one in the hope that the culprit is something non-essential which can be remove
I simply can't do this, it is a laptop and if I could afford replacement parts for it I would have replaced the entire unit.
Having dealt with this on and off for the last year I have done a lot of the possible fixes, including tearing the machine apart for the thermal paste and general cleaning. The electrical engineer that helped me didn't notice any piece that looked damaged externally. This of course doesn't mean there isn't something damaged but nothing looked like it had gone bad. Right now I would just settle for a way to identify what is wrong with the machine. Again it usually seems to be slightly more intensive things like videos or games, as well as occasionally with really busy sites like the weather channel with the map open, though that hasn't happened in months it did happen prior to replacing the drive the the first quarter of the year.