Since we have no idea what model this is it is hard to diagnose it. I'd recommend trying an external usb mouse and keyboard if that is an option on this unknown model. If you can get in to the device you may be able to clear the drivers that are faulty to fix this issue.
it might be stuck in standby mode or the screen might be bad. Try a full reset by holding the power button and the volume up for about 15 seconds and see if it will reset to the surface logo- if it does it should boot from there. This might be one of those surface stuck in standby glitches that can be fixed by a full power off with the above step.
I'd recommend getting ahold of a used surface pro 3 that has a bad digitizer, but a working screen and a good working surface keyboard. I have a surface pro 3 that has a bad digitizer, but the screen is fine and with the attached keyboard it works just fine for navigating around. If the ssd is encrypted you will need to carefully put the working screen on the locked unit and go from there. Other than that you are looking for a replacement digitizer/screen assembly on feebay with rush shipping and hope it works for the $400+USD. Hope this helps...
I would recommend reseating the digitizer ribbons again and checking them carefully- I had the same issue due to a slightly ripped cable- it worked- but it was ripped just enough to cause random phantom touches.
Power button assemblies are available on ebay, but to fix it- you need to completely remove the screen/digitizer- not an easy task and not recommended unless the screen is already broken and needing replacement anyway.