Im sorry to say there is a whole other thread devoted to your problem and it is many many pages long. In the meantime some fellow through a stroke of luck found out that by blowing real hard in the ports on the same side of the camera as the shutter switch the shutter button began working again.
If your camera is still under warranty I suggest filing a claim immediately.
You can search out that other thread but in a nutshell a whole lot of people have had the same issue as you. Forcing air into that side of the camera seems to be a fix, temporary one.
Here is the link to the page where the fix is mentioned at the bottom of the page and continues on for more pages and messages
http://forums.usa.canon.com/t5/PowerShot/shutter-release-not-working-S100/td-p/12213/page/15
