Device not turning on or charging

I assume you went to the local repair store because this device no longer have warranty.

If it is indeed a motherboard/main board damage, then xiao mi would have replaced it (motherboard) entirely, fixing the motherboard itself is a lost cause, and even if it does get fixed, it is likely to deteriorate further and fail overtime.

Is it possible to retrieve your files from a damaged android device? if the device can be plugged into a computer and if the computer can recognize the device then the answer is YES, BUT if not then the practical answer is NO... unless Xiao Mi has a device that they can connect to the soldered memory chips and extract the files from there. I havent heard of anyone doing that except for NSA spies and hackers.

I suggest you keep a back up of your files in the future, saving them in cloud storages (google drive, etc). They offer certain amount of space sufficient for an average person for free.