Thanks for all replies. The laptop is a Dell XPS M1210.

The reason I've come to the conclusion that the problem is more
serious than the power supply or a loose power jack is a few postings
around the net such as these:
http://getsatisfaction.com/dell/topi...t_r ecognized
It's a problem which a few people have and no one seems to have found
an easy solution by just soldering on a new jack. The advice from Dell
(according to those posts) seems to be that a new motherboard is
needed.

Michael, thanks in particular for your offer to post information about
circuit diagrams and software concerning charging batteries. Frankly
that sounds like it's going to go way over my head and be beyond my
minimal understanding. I guess I was hoping someone would tell me that
I could just put 12v DC across pins 3 and 5 for two hours and charge
it and keep the laptop working that way. It sounds like I was being a
little naive, so I thing it may be a trip to the repair shop and a new
motherboard (or maybe just a new laptop!).

Cheers!

Martin