It is the 2.66 GHz Core i7 model. I say it is not the OS because it crashes with two different OSX boot disks and during...

See 2010 MacBook Pro shutdown during boot (OS is good) A bad keyboard can lead to these symptoms.

I sent this laptop to a second shop for repair. They told me the logic board was ok but the keyboard was bad. They said the first indication of the keyboard failure was no response to the brightness keys. In the 30-60 seconds that it would run I never noticed a problem with the keys but never tried to adjust the brightness. After the repair, the laptop works normally: and the cap overheat Nvidia GPU problem is gone, due to the repair from the first shop. @Dan has been trying to work out a model for the root cause. It seems that as heat (or charges?) built up it triggered the keyboard failure: some short or false button press combo that led to shutdown. It is interesting that target disk mode and AHT were able to keep running. My guess is that either they don’t activate the keyboard the same way or they don’t generate enough heat to trigger the failure.

See Breville Dual Boiler (BES900/BES900XL) Group Head Collar Insert Replacement Guide

Mine is leaking water rather than steam. But maybe a water leak comes from the same root cause? I determined that the plastic handle has worn and the steam control lever now moves beyond the valve's fully closed position to a position which is partially open. So if you back up the lever a few degrees it might stop the flow. I have yet to figure out if there is a way to replace the plastic lever/handle piece.