Xbox One Power Supply Turning Off When Plugged To Console

Hi all,

I recently got a free Xbox One in a rather questionable (dirty) condition. I was given a power supply with it, and I attempted to plug it in. When I plug only the power supply in, the LED turns on and stays on. But when plugged into the Xbox, it will turn off after a moment. The power supply was tested with another Xbox One and was operational when plugged in. What could be the issue, and how can I troubleshoot it?

Thanks!