Hi pisanivito, I believe your broken display is an LG sourced display. I have attached an image of a Samsung display. The differences are subtle and they are interchangeable, provided you use the correct connectors. If you choose to use the IFIXIT display, it will be compatible with your Surface Pro 4, but you will need to order the correct display connector PN: X937072-001 . The N-Trig Digitizer should just be a hot-swap and although your connector for that looks different from mine, it should work with a Samsung display just fine.
I seem to be having a similar issue. I have yet to find out what is wrong. If you ever find out what is wrong let me know; I have heard it could be a blown resistor but have yet to find one that does not give a voltage readout.
