My very expensive laptop does not turn on anymore?

I've been charging since yesterday and it still does not turn on since yesterday!

Nothing starts not even the fan!

Did he fall down before you or something?

No

And the temperature is also very hot even if it is out I measured 60 ° C.

I do not know what that is?

Remote diagnosis is always difficult, would say that something either your power supply or your motherboard / cpu has grilled

Then it is quite possible that your fan is simply vereckt, I think that you use your "expensive" laptop on the bed or couch, so comes much more dust and dirt in your laptop housing and sets your fan to, up to the Time when he smears because he gets too hot or shuts off for safety's sake.

I type on battery empty and power supply delivers no more power…

as the first time check whether the power supply still power, so check the outlet (rather unlikely, but very light to check, for example, with a floor lamp or something)

then look again, whether the plug in the power supply properly drinne sits, if that is the case, it's a bit more difficult. Measure with a multimeter to see if power comes out of the power supply…

for everything else you will need a professional on the spot.

Battery out and try to start only on power supply. If that does not work, there's probably a hardware defect. High heat during charging indicates high current. Either because the battery is defective, or the electronics in the laptop has a short circuit. Listen to the power supply, if that starts to fever or pulse, if you plug in the laptop plug…