T i m wrote in
:

Cheers, T i m


Get a competent technician to take the laptop apart and resolder all the
connections between the power jack and the circuit board it is SUPPOSED
to be soldered to. They get a hairline crack in the solder because
that's the only thing holding the connector to the board. These cracks
can be so thin you need a jeweler's loupe to see them, if you find them
at all.

Resoldering the connector to the board fixes the problem.

The competent technician will, of course, load test her AC power supply
before tearing into the computer, bending and pulling hard on the plug at
the computer end to make sure the wires inside the plug and cable have
not been broken, another common source of intermittent power, but you did
say it was powering the computer so that's probably not the problem.
There is a switch telling the computer the power supply is plugged in on
many models moved by the power supply plug and that switch's connections
may be intermittent.