|"It has not been dropped or damaged in any way"|
Does anyone else have access to this netbook ?
If yes, you can't be 100% sure of that.
It's very common for people to unplug the AC adapter by pulling on the cord rather than pulling on the plug at the laptop jor netbook ack .
That eventually damages either the wires near the plug inside the cable (most likely), or the plug on the end of the cord (less likely).
After a longer time of the user doing that, it's common for the jack in the laptop or netbook to have been damaged, or to even be broken off it's connection to the jack inside the laptop or newtbook.
The jack the AC adapter plugs into should not be loose in the netbook at all.
There is a "charging" led on the netbook that should come on at least briefly when you first plug in the AC adapter when the battery is installed, even if the battery is fully charged.
If the wires inside the cord or the plug or the jack is damaged, that led may come on / go off when you wiggle the cord near the plug, or wiggle the plug in the jack, when the AC adapter is plugged in.
If the wires inside the cord get damaged such that they are shorted, that will burn out the AC adapter in a short time..
Does the AC adapter have an led on it ?
If so, does it light up ?