I would try this:
Make sure laptop is powered off - if its on, hold down power button until it shuts off.
Then to verify screen is working I would try the Lenovo LCD Self Test:
"Use the following steps to run the LCD Self-Test:
Turn off the computer.
Connect the AC power adapter.
Press Fn, left Ctrl, and the power button at the same time. ...
The test lasts for about 20 seconds and then the computer turns off automatically, or press the power button to exit the test."
It just shows the 5 single colours on screen. Black, white, red, green, blue.
If that works, then the screen is ok.
Turn it on again: Do you hear/see any activity? Fanspin, lights etc.
Turn it off again, if needed by again holding in the power button until it shuts off, if needed.
Try power refresh - unplug, hold power button for >30 seconds, then see if it turns on by pressing power button.
If not, can try full power refresh, that involves opening the back and disconnecting the battery, then holding power button in for >30seconds
[guide|148435]
Up to "Step 3 - Unplug the battery connector in the direction shown by arrow", (no need to remove screws/remove battery)
Then try turning it on by connecting AC adapter and pressing power button. If it comes on, great! Shut it down, reconnect battery, close case. Turn it back on, should be good to go.
If still no luck, there could be deeper issues to look at.