I didn't say my power adapter doesn't work with my laptop. I simply said my system with its power adapater or its battery wouldn't turn on. I am not too sure whether the system itself or the power adapter is the culprit.
I didn't usually work with the battery inserted. I usually had it charged up and put aside and worked with the power adapter connected all the time. I only used the battery where I couldn't get the mains.
My daughter's computer battery wouldn't work for a few minutes since long time ago because she always has the battery plugged in and it now can only store very little charge. She had already replaced her power adapter with a compatible one for ages.
What I did was, I simply swap the power adapters and tested them. I must admit I do not remember for sure now if I have the batteries of both systems out at the time of testing.
Since my daughter is not living with me, I have to wait till I see her and test the system again. I shall make sure I have the battery off and wiggle the power adapter. I shall report back.
I suppose I could be too quick to conclude that it was either the motherboard problem or the connection of power at the motherboard after my test using my daughter's system.