In the beginning it cost to shut down, but then begins to shut down faster. I checked the CPU temperature, but is within the normal, including the thermal paste has changed both the processor and the BGA. I also left the battery out. Only if it is cold solder BGA problem.

suspicion on NVIDIA Quadro NVS 140M

You have time to measure the temperature of the video?
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If open bios setup, your laptop turns off ?

It is noticed that when you remove the heat sink of the processor and nvidia the eraser was torn in the middle which probably did not help dispel the right heat. I would try to replace the dissipative rubber (a notebook is used in the service and my boss decided not to invest in maintenance because it is an old notebook) but decided not to invest in repair.

So ..... not repair?