You can use reflow to fix ANY top soldered board including automotive and television applications.

HP laptops are tops soldered at the factory, meaning they are baked. A temporary fix if it dies on the road is using a hair dryer. The permanent fix is by rebaking it. https://www.youtube.com/watch?v=G65-ncBxdHA

re bake it https://www.youtube.com/watch?v=G65-ncBxdHA

I have found that often the surface still charges even though it's charging led is not lit. Reach down and see if the power supply is warm. A warm supply means a charging surface. You should be able to pull your surface battery out of deep sleep using a USB cord plugged into your computer or a car outlet. Another way is to buy another AC charger and cut the plug off.