Of some significance is whether the braid screen encloses 2 or 3 insulated
wires, if its 3 the PSU has an earth if not its most likely "double
insulated" as they'd unlikely rely on the mechanical construction as the
sole means of earthing the appliance.

Check continuity from the exposed braid to the earth pin, if its connected
fine, if not your options would be limited by whether the plug is molded or
dismantleable.

Thanks for that, but I didn't understand the reference to the earth
pin. It probably doesn't matter because, if you read the OP, you will
see all the wires are enclosed together in their own insulation so I
don't know how many there are.

But thank you all for taking the time to help me. I think I have the
answers now which I will post here perhaps to help someone else
sometime.

I have obtained the laptop and the charge light does not go on unless
I manually connect the severed braid with a piece of wire. Then the
charge light does go on. I am assuming the laptop is now charging
normally since I don't, at the moment, have the password so can't log
on and see the battery status indicator.

I cut away the rest of the rubber casing (about 1/4 inch) at the
charger end to expose as much of the braid as possible and stripped
some insulation off the cord. It's not so much a braid or mesh... more
like many strands of silver wire running the length of the cord and
all around it. I'm guessing it has to do with the RF stuff. Anyway, I
soldered a length of wire to both sides to connect the two and taped
it up. No flickers when jiggling so it seems like a workable repair.

I would have bet against that braid being part of the electrical
connection (and lost) but that's how we learn stuff.

Thanks again.
Mike