Early 2015 13" MacBook Pro Retina Won't Power On

Have you tried the Apple Diagnostics? This source has instructions for the Apple Diagnostics which are for machines after June 2013 so it should work on your computer.

If this doesn't help you and if you live near an Apple Store, take your computer to the apple store and just ask them to check it for you. Explain your problems and see what they say. Maybe they'll find the problem. Tell them you ran Apple Diagnostics but if offered no help.