Hmm... sounds like a little too much pressure might have been brought to bear on the button. Any time I have tried this, I have had no problem, but I am fairly cautious about how hard I clamp the thing, typically I will use an elastic band or something fairly flexible.
The switches in these cameras are not the most robust examples on the planet, and in some cases, they consist of nothing more than a small thin metal (or in some cases silicon rubber) disk, which deforms when pressed, and pops back when the pressure is released.
In the cheaper models, these disks are typically attached to a sheet of adhesive tape above the circuit board with the switch contact tracks on them.
In the case of the D10, they are slightly more substantial, but not much.
In other words, they can be a little fragile.
I don't have a D10 to hand, but depending on how adventurous you are feeling, and how easy it is to get in to the camera without damaging anything, (including the waterproof seals in the case of a D10) you may be able to pop the button back up with a small pair of tweezers or something similar, or even replace the button PCB, which will be available on ebay
no doubt, but at a price (picture below).
The individual switches are only a few pennies each, but replacing them requires some skill with SMD soldering. Those little boards are very easy to fry if you are a little heavy handed with the heat.
All of the usual warnings about voiding warranty, everything being at your own risk and high voltages on the flash circuitry apply if you do decide to pursue this idea.
If surgery on the poor thing sounds like it is too risky, then I would go with waterwingz's suggestion, and use a script, and one of the other buttons to switch it off.