Xbone powers on for 3 seconds and then powers off.

I picked up a used original Xbox one and it's not powering on properly. It comes on with the normal sound and light, but after 3 seconds, it shuts down. The power supply appears to be working properly, so I opened up the console and cleaned it thoroughly. That made no difference. While it was apart, I noticed that the cooling fan slightly "bumped" when power first came on but it doesn't actually spin at all. I tried turning it on while manually spinning the fan with compressed air, in case there is an rpm sensor that wasn't being satisfied to keep it powered up, but no joy.

My next "guess" is to buy a replacement fan and see if that fixes it, but I wanted to get some more info first, seeing as this is my first experience at all with this system.

-Is the fan supposed to start spinning immediately?

-Has anyone else had this problem, specifically 3 seconds on and then shutdown, and if so, did replacing the fan fix the problem?

-Has anyone fixed this particular problem any other way?

Thanks for the help.