New batteries come in higher and are cheap. I'd toss a new one in just to remove that as a possible issue.
So my laptop (Toshiba Satellite L775) doesn't boot, unless I remove and reinsert the cmos battery (located behind the ram). Also the laptop screen doesn't receive power. After the cmos trick I don't have to press the power button and the laptop boots the moment I connect my adaptor. I am able to use my laptop by connecting an external screen.
Things I did:
-check voltage on my adaptor (A ok)
-check CMOS battery voltage (3.08V)
-check the power button by checking the resistance with a multimeter and seeing it go from infinity to zero when I press the power button
-check the voltage on the wires that power the screen (0 V DC, is the DC a correct assumption?)
-pushing the power button repeatetly (no effect)
-holding the power button to clear the remaining power from the board ( without the battery/adaptor), this didn't help but was neccesary to make the CMOS-battery trick work

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