To me it sounds like the battery. I have never owned a laptop. But a lot of electronic gear that use both ac and DC use the battery to filter the raw dc coming out of the ac/dc converter. So if the battery is going, you may be getting unfiltered dc to the motherboard. Have the battery tested, some rechargeable battery develop a memory, which keeps them from charging/discharging properly. Sometimes this can be fixed by discharging the battery completely, and then charging it completely, do this several times and you may be able to fix it. Again the place that tests the battery should be able to do this. You need to set up the electronics to do this so I would not do it myself. Sometimes you just have to get a new battery.
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