My laptop won't turn on when it's plugged in

@uzairhavegyatt Start off with the easy things. Disconnect the power from the computer by unplugging the power cord from your computer. Disconnect all external devices from the computer. Now hold the power button depressed for about 30 sec-1 min. Reapply the AC power adapter and see if your computer does show any sign of life.

First you want to check your power supply. Make sure it has the proper voltages. Check to make sure that connectors are not bend etc. Check the DC-in jack of your laptop. Make sure there is no corrosion, debris etc. that prevents it from working. Clean it of any debris etc. use a few puffs of air to clean it out. If none of this works, get a ammeter and see if your laptop draws any amperage from the charger. After that, you need to check and see if your motherboard even gets power. For that of course, you need to open it up. Post Some good pictures of what you see. That way we can see what you see. Adding images to an existing question

We will need to know the exact generation of your E14 since there are a few different ones. Use the Lenovo ThinkPad E14 Gen 2 Hardware Maintenance Manual to work on it. Start with page 25. Let us know what you find out.