If you boot it up with the power supply connected and disconnect it when windows is running does it go off aswell?

If yes then I would guess that something like the battery charging circuit on the mainboard is defective, so your best chance is the support from the place you bought it from.

If they don’t offer you warranty repair/replacement you…[Read more]

I don’t think that is normal that its hot while its charging turned off .Maybe you didn’t shut it down properly ?.And when you turned on i assume the fans cooled it down.At the top above the keyboard its normal that’s its warmer or hotter than other area because the exhaust is there (between the hinges ) and also the cpu and gpu heats up that area…[Read more]

Yes, but Surface is always better.