Have you checked the mains voltage at the socket you are using? Your PC/laptop may not recognise a low voltage but your screen supply may automatically compensate.
As a general rule I believe it is suggested the battery from a laptop be charged and stored in a fridge (not freezer!!) if the unit is to be used continually on mains power. Extends the battery life.
You should be able to determine what the "little red light" is by examining its location on the case.