he tried 2 adaptors. my bet is either the one line communication reciever on his mobo broke, and is no longer recognizing adaptors; or the charging system is shot. with dells, either can be the case and they refuse to admit that there is a defect.
as for the heating issues, the newer dells use a tighter cooling fin pattern for their heatsync assemblies than most companies, and then they used to on older laptops. this is great for cooling (surface area, all that stuff) in a clean environment, but once you put it in the place where laptops normally live (someone's jeans, sucking air through the comforter of a bed, that dusty desk we all use...) the heatsync becomes an air filter, pulling the dust out and forming a brick right in the airflow. the only solution is to completely dismantle the machine, remove the dust block, clean the fan, and reassemble. this will allow the air to cool the machine again. just remember to use thermal grease when reinstalling the heatsync to the processor, or the only thing that will happen is the re-location of your cooling problems.
hope this helps until Dell fixes this problem, sorry I have no good solutions for your charging issue. my only help for that would be to write Dell a letter explaining a particular design defect that caused the problem and demanding they fix it (please don't forget to mention that official government guy that is in charge of consumer goods whose title i can't remember right now, that gets responses quickly)