[TECH] My Xbox One power supply turns off when I plug it into my Xbox, preventing me from turning it on. Is there any way to fix this manually?

My power supply is working fine - when I plug it in the orange light is on - but when I plug the other end into my console the light disappears after one second, and my Xbox One won't start up. I contacted Microsoft and went through some troubleshooting steps, after which I was advised to send my Xbox into them for service/replacement which would cost me £91. Is there any way to fix this problem manually?