Welcome morges1
Greetings morges1, welcome to Flyertalk, and welcome to the BA board. As a very experienced traveller on oneworld it would be good if you could stick around here since I am sure you can give us many insights of value, in addition to this offering. Welcome on board.
I have a PC that consistently gives me very similar problems to yours, it is an elderly HP laptop. If it was not 100% charged it would typically short the plug immediately - and to reset it I'd need to stick in another device. If it was 100% charged then it would trickle down the power or not work at all. Same on Lufthansa, incidentally. Now I happen to have to have a wattage meter and it was running at 78 watts, which is too high for aircraft, so I got another adapter which came in at 62 watts - marketed for travellers and a lot lighter - and all has been well ever since. Incidentally I did find that I could minimise the problems by dis-enabling both bluetooth and wifi modes, which you are supposed to do anyway, this brought the watts down a bit.
I never have a problem with my Samsung Netbook (which in any case can go off batteries for 8 hour anyway), and I know I used both laptops on one of the services listed above!