Bad motherboard wont charge battery

Just remove the hard drive from the computer, it contains all your data.
The only problem is when they fit a new motherboard and you install your hard drive back in the computer, it may not boot up because the motherboard maybe slightly different between the original and new motherboard.
I suggest you get them to install a new hard drive and install your original Windows onto the new hard drive with the device drivers and your programs. Then purchase a USB hard drive adapter case and put your old hard disk into this USB case, then you can use it as an external USB hard drive, which will contains your data. You can delete the Windows folder and other non data folders off this hard drive to free up disk space..

It may be the DC to DC circuit, which is in the motherboard or could be just the DC power jack.
If you gently move the power plug of the laptop left, right, up and down and you see the LED lights changing that, is a sign of a lose DC power jack to fix it, you will either re-solder or replaced it.

Good luck
N Sabre