M1710 charging very slowly

A few months ago my XPS 1710 slipped off the coffee table and fell about 2 feet to the carpet. No serious damage seems to have occurred but there is a slight oddity. It now charges the battery very, very slowly. It takes over 2 days to get to 100% from flat.

And sometimes, not often, it looks as if the battery isn't connected at all. That is, if I pull the power lead out everything just shuts down no matter what the state of the battery. Usually this corrects itself in moments.

This  happens with more than one battery, so I'm guessing the drop did something to the connections to the battery. Could the impact have cracked a solder joint, increasing its resistance?

Would there be any mileage in trying to remake or reflow the solder around the battery and power connections or would I be risking rather worse damage?

Which has given me a thought about another problem with the laptop. The Ethernet socket doesn't work. Could that be dodgy solder?