I agree with sdromel - good chance the problem's in the on-off switch. The mode/on-off dial assembly is a flimsydesign. It consists of athin flexible printed circuit and some plastic hardware vibration welded(?) to the main body. (Incidentally the switch/modedialassembly is easilybroken off the C2100 camera body - don't ask how I might know!)
Anyway it's design renders the switchsensitive to moisture, dirt, etc.Might be worth shooting a bit of aerosol electronic contact cleaner around the base of the switch, working the switch a few times then blowing it out with canned air before the cleaner evaporates.
Also check the battery contacts both in the battery door and up inside the body. I had an earlier digital camera (Kodak DC210) fail completely. Problem turned out to be a single battery contactstrip that for some reason had become "sprung"and was no longer touching the battery. Pulling the stripback into it'scorrect postionbrought the camera back to life. ...FB