Toshiba satelite 4200 boot up problem

I have two toshiba satelite 4200 series laptops , that can power up then after a while they go off completely on their own and when you try to power them up they cannot .

I have changed the batteries as they cannot power up without a battery .

changed memory

changed the processor

all this in vain

I know techs will say it is the main board , then why is it that when you leave them for some time they boot-up and stay for a while then go off and why is it affecting toshiba satelite series 4200 series only.