If you have a DMM (digital multimeter) first check that the charger’s output is OK. It should measure +20V DC. (see image below)
If there is no output or if it is <+20V DC then this may be why the laptop shows no indication of any power and also the battery may have become depleted due to not being charged. Try using another compatible charger and check if it works OK. If it does allow the battery to fully charge before using the laptop on the battery only.
If the charger tests OK then here’s the hardware maintenance manual for the laptop. This will help you to open the laptop so that you can access and test that the DC-In jack and cable are OK (see image below).
Once you have accessed the cable, unplug it from the board and then use the Ohmmeter function of the DMM to ensure continuity of the red and black wires from the jack to the cable plug. If one of the wires is open circuit (most probably in the jack itself) then the cable/jack component module will have to be replaced as it cannot be easily repaired. The image below also shows the part number for it. If you search online using the part number only you will find suppliers of the part.
If the DC-In jack and cable tests OK then there is a motherboard problem. On p.39 of the manual you’ll find the necessary pre-requisite steps and then the procedure to remove the HDD so that it can either be installed in a desktop PC as a secondary storage drive or connected to a laptop using a suitable enclosure so that your data can be retrieved from it. Search online for how to connect a HDD from a dead laptop into another computer (example only)
(click on image to enlarge for better viewing)