Can you please describe the issue more carefully. Do you mean that you can't turn your laptop on? What happens when you press the button? Does the light on the power button come on? Or do you mean that when your laptop is on, the power button does not trigger a dialog that you are used to getting (e.g. the shutdown/restart dialog)?

Yes sorry for the short report.

The button hardware is working: I can power the laptop on, and I can use the emergency power off (keeping it pressed for a few seconds). But it is not detected by the OS, so it can't be used for a normal power off or hibernation - the power button doesn't trigger a dialog. When polling various /dev/input devices, nothing happens when I press it.

What happens when you run "xev -event keyboard"? I get the following output:

I get the following output (but I have a different XPS 13 model from you, 9343) after I press the power button:

MappingNotify event, serial 28, synthetic NO, window 0x0,
request MappingKeyboard, first_keycode 8, count 248

KeymapNotify event, serial 29, synthetic NO, window 0x0,
keys: 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Also, what is your BIOS version?

xev says nothing, like I didn't press the button. It otherwise works. My bios is 1.2.3.

Oops in fact xev is moot only under Debian. Under Ubuntu it works and says:

FocusOut event, serial 39, synthetic NO, window 0x2200001,
    mode NotifyGrab, detail NotifyAncestor

FocusOut event, serial 39, synthetic NO, window 0x2200001,
    mode NotifyUngrab, detail NotifyPointer

FocusIn event, serial 39, synthetic NO, window 0x2200001,
    mode NotifyUngrab, detail NotifyAncestor

KeymapNotify event, serial 39, synthetic NO, window 0x0,
    keys:  2   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   
           0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   

OK my bad. I have been mislead because under Debian it doesn't work at all. Under Ubuntu it works, the OS can see the button. Now hibernation doesn't work, that's why I thought the button stil didn't work.

I'll go check why hibernation doesn't work, but that' another problem.

Do you mean suspend? Hibernation has always been difficult with Linux, especially if you happen to use full disk encryption.

I mean hibernation. It just looks like it's not configured by default, as I don't use FDE it should work.

I'm more worried of the sad state of Debian on MTT 9360. It's completely unusable.

Can you issue a command to the kernal via the power button? 

 $> sudo pm-hibernate

http://www.linuxandubuntu.com/home/how-to-enable-hibernate-in-ubuntu-linux