My coworker and I both got new XPS 12 9250s from the Microsoft website. Supposed to be their signature edition. He is having a problem with his holding a charge. It will not hold a charge for more than a few hours even when it is powered down. So if you put it in your bag in the evening charged and go to work the next day, it will be completely dead. I had the same problem with mine.
Today (only a few days old) this machine is doing exactly what ElAguila is describing. Only difference is that mine will not even buzz when you hold down the button. I have had it plugged in and the screen laying down on my desk all morning. The thing is warm so something is happening in there. But no response on the screen at all.
Don't know what to say about your coworker's PC, other than questioning if he simply closes the tablet onto the keyboard resulting in a sleep state or actually powers completely down before folding the tablet onto the keyboard. My XPS 12 9250 lasts a bit less than 4hrs. Do you feel a small click in the process of pushing the power button? The outer switch pushes a tiny roun toggle switch on the motherboard. These power buttons on our 9250's should be pressed with the fleshy tip of finger, definitely not with a finger nail. I found that out when I had to repair my power button. The outer switch slipped under the inner switch preventing the preventing the toggle on/off. I had to take the switch off and then made a paper template which I used and added to the small piece of duct tape cut in the exact shape of the underside of the switch where it contacts the motherboard. This extra bit of thickness (I had to pierce several holes in the paper and tape because of alignment pins and the small screws) slightly lifted the switch to center it directly to contact the small round toggle on the motherboard. Possibly your power toggle was and still is in the power on state, unless you can actually feel that small click I mentioned. If the click is there, then your power switch is OK.
Sorry for the misspelling of round and repeating preventing twice.
It would be good to hear back from ElAguila and others to expand or comment on answers they have checked. Like "It was returned to Dell for repair", or "total loss", or hopefully a successful solution,