There is no "mid-2013" MBPro. There is an Early and a Late 2013 model which are both Retina models. Or do you mean a Mid-2012 non-Retina model? The exact model is extremely critical. You can get the exact model by clicking the Apple menu and selecting "About This Mac" or by entering the system serial number here:
Check Your Service and Support Coverage - Apple Support
Try running the Apple Diagnostics to see if any hardware issues are detected. Make sure the charger is connected before running the diagnostics or it will cause an error.
Try booting into Safe Mode to see if you can boot & login into the desktop.
Try booting into Recovery Mode (Command + R), or even better into Internet Recovery Mode (Command + Option + R) so you can try running Disk Utility First Aid on the hidden Container. Within Disk Utility you will need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Even if First Aid says everything is "Ok", click "Show Details" and scroll back through the report to see if there are any unfixed errors listed. If First Aid is unable to repair any errors, then you will need to erase the whole physical drive before reinstalling macOS & restoring from a backup. However, I highly recommend you create a bootable macOS USB installer first if you can boot this laptop since otherwise you need a compatible Mac since there have been a lot of reports that it is no longer possible to reinstall macOS from Recovery Mode/Internet Recovery Mode.
Have you ever had the battery replaced? It is possible the battery is bad which can prevent the laptop from powering on or even charging the battery. You can try disconnecting the battery from the Logic Board and trying to power on the laptop using only the charger. Just make sure not to allow any metallic or conductive object or surface come into contact with the exposed internals.
FYI, you should always have frequent and regular backups. Many times it is impossible to recover any data from an SSD or any of the newer 2016+ Macs when they fail.
