DC input plugs can be mangled into connecting better.
and that is what could happen to it trying to get it to connect better.
if they changed one plug, or say the source of the wall-wart , it could be slightly mismatched and still "work" by definition of working.
there is no li-ion (type) of danger of it becomming dangerous because of the disconnection, the charge is voltage max regulated.
first is it the very TINY connector? because that one is , uhhh, how to say, barely connecting as it is
if you want to mess with it, unplug it
and here is a few things which only one is usually neeeded.
check how the plug slides in, and hits the center pin then look for the side swiping connector that contacts the outside of the pin, is any plastic of the case hindering the travel of the plug from going in and making contact.
on the Jack on the case, there is a pin that goes down the center of the plug,. is this center pin making good contact?
IF the pin is a "split" pin then you can shove a razer or exacto knife into the split and increase the split pin diamater a tiny bit. an i mean tiny push, because if you bend them more than that, then you wont get the plug on, and have to bend it back. if you bend it a lot more than that, then stuff will be falling off before you get the plug back in. even with stuff falling off you can usually make contact
then notice where the side swiper is that touches the outside contact on the plug, look straight down where the plug goes in.
if you very slightly bend the pin towards the side swiper , the plug will go in at a slight angle pushing up against the swipe contact better. and the offset angle of the pin then will also jam the pin tighter where it connects down the center of the plug.
if there is no movement clearance, for the plug to get closer, then you gotta try to move the contact itself instead.