In case Lenovo thinkpad laptop doesn't turn on, first thing you should check is the power supply. You need to plug in the charger properly and make sure that there is a sign of charging. If you have an option, you need to use a different working outlet and disconnect all the attached devices. Then you should press the power button only one time and give it a few seconds. In case your laptop does not respond at all, you need to press and hold power button for around 10 to 15 seconds, release it, and try powering it again. In case your Thinkpad laptop allows you to remove battery, doing so might help in solving some basic power issues.