Hi MinShih,
What is your complete model number, Lenovo ThinkPad X1 is a family of products?
Is this computer new?
Have you checked there is no dusk build up between the power cord, charger, and the computer where it plugs in?
Does the charger have an LED light on it to tell you it has power?
Have you tried a different power outlet on the wall?
Have you removed the battery from the laptop and checked everything is OK in there?
If it was not charging, why did you leave it in that stat until it ran out?