Lenovo T420 won't power up

Hello,
I have Lenovo T420. Last week I shut it down, and the next day it would not turn on. No lights to show it was charging or plugged in. The power charger works fine on my other Thinkpad. The battery is new. NothingvI tried worked. All ofca sudden, after a week of not working it came back on. I used it all evening with no issues. I shut it down and now have the same problem: it won't start. Any help would be greatly appreciated.