... the x220 (i5, 4287-59G) sometimes will refuse to boot. Pressing the power button does nothing. I will try with battery in or out, re-set the BIOS, and so on. ...
If you get as far as being able to reset the BIOS, then the power button turned on the machine and the machine has booted already. Do you mean that the operating system will not start loading after the machine has booted ..or.. do you mean that the machine is dead because the power button does nothing?