Common issue for all laptops but I have personally experienced this with T440s, T450s and some HP laptops.
Laptop has a black screen with no indicator lights lit up. Powering on with power pack attached or from battery power laptop is unreponsive and nothing happens
This is usually a very quick fix, you can remove or disconnect the battery and then hold the power button down to remove any stored up or residual power left over in the system preventing POST.
Step by Step (T440s/t450s and similar laptops)
1. Remove Battery
Remove battery from laptop
2. Remove Back Cover
Undo all the screws on the back of the laptop and then use a spudger to slowly pry open the back cover, see image below for order of steps.
3. Unplug Internal Battery
unplug internal battery , image shown in number 2
4. Hold down power button for 60 seconds
5. Retry powering on with all batteries disconnected
that is all for today , hope that helps for all those whose laptops won't turn on but display beeps or warning lights visit your manufacturers website to identify the issue.
Ive also heard of people getting laptops to boot by removing the ram and trying to power it on , or simply reseating the ram.