Yesterday it powered off 5-6 times, all of sudden. The battery in the laptop has been empty for several years so it is always plugged to the wall. Today, I bought a new charger for it but the same thing happened again. Sometimes the screen gets garbage a little time before it powers off.
The windows event log do not have any HW errors.
@jonne suggested in Discord “Powering off sounds like a safety feature, either heat or voltages”. So I will next try to open the laptop shell and cleanup the PCB and other electronics from the dust to prevent overheating.
If you get a powerdown due to heat issues, it is usually pretty systematic. You startup the PC and after approximately x time it shuts down.
Temperature protections are built into the BIOS and motherboard chipset. In modern boards, there are several overheat triggers in CPU, GPU and case.
Heat issues can also appear in such cases where BGA chips (typically GPU) have breaking solder joints due to thermal expansion. In these cases, again, the problems are often related to computer temperature. But I have not seen that eg. failing GPU causes shutdown.
What I do know however, is that faulty voltage rails (3.3V, +5V, 12V, -12V etc) that are giving wrong voltages will trigger safety shutdown in modern PCs… AND … come to think of it … so will short circuits in things like USB voltage rails.
Now, lets assume one of the decoupling / filter capacitors of one of these voltage rails is dying. That will lead to uneven voltage on one of the rails. If you get corruption on screen, it means the GPU is struggling to read memory clearly. This is turn can be because the logic level is uneven or too low - a condition that would soon trigger an emergency shutdown.
I advise to open up case and do a cleanup of fans and heatpipes. Also remember to check that fans are turning on, because faulty fans (no rpm signal) will also trigger shutdown on a modern PC
I can say it is pretty systematic. It powers off about 15 min or so after power on.
You mean that e.g. a faulty USB device/cable could cause it?
I have no idea how to check this
I can at least hear that the fan is running when the laptop is powered.
I guess the compressed air is a good way to dust off.
Yesterday, I opened the laptop shell and used compressed air to dust off the internals, mainly cleaned the fan intake holes. There was not very much dust. I also switched to another USB mouse.
After that I was able to work several hours without any poweroffs! At the first boot I saw screen garbage shortly, but after that everything was fine. I tried to give some CPU load by running the Pokitto simulator at the same time as compiling with FemtoIDE (Femto usually takes all the CPU resources in my underpowered laptop).
So far so good 
It sounds like it is affecting the graphics card? A faulty battery heats up and inflates with gas so it might physically damage more stuff (because it heats and bends stuff).
I have a laptop that has been running for 3 years with lots of issues (battery bulged first, cpu fan failed, graphics card failed, usb3 ports burned because one short, etc…) so I have 2x 12 CM fans pointing to it and a wooden rod to lift it. It does not affect the integrated intel graphics, only the nvidia one, so it kinda works ok, but I see purple/pinkish waves/artifacts on boot and shutdown and fullscreen garbage/system hangs if by mistake moved one of the external fans away.
That’s my kind of style. Except I use icepacks from the freezer!!!
But then you need a complicated conveior belt system that constantly feeds them 
