The Laptop cant turn on.

@jerrysililo this "used to get very hot" and your computer no longer turning on sounds like you have a failed processor. You may also need a new fan and will definitely have to get new thermal paste on your heatsink. Those are not preventing your computer from powering on but may have been the cause for the failure. Anyhow, start with the basics.

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

Next 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 and if your processor may have severed terminal thermal failure. It fried. 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

Use the ThinkPad X250 Hardware Maintenance Manual to work on it. If you are stuck anywhere, post some pictures so we see what you are at and cn hopefully help you out further.