Sounds like the battery or lighting connector assembly went bad. More than likely it was your battery. Try the apple store first. If it's the lighting connector assembly you can change yourself. iPhone 6 のLightningコネクターアセンブリの交換 Here's the guide. It's not bad to change out, just follow the guide. Hope that helps.
A few ways to do this. If you have buy a bridge usb cable you could hook it up to another pc and transfers it (not a standard usb to usb). I don’t know what time of hard drive is in the surfaces but you could uninstall it then hook it up to another pc. If you have a remoting app like google desktop remote install you could share your hard drive then map it to another pc on the network. Let me know what your thoughts are for what process to proceed on so I can help further.