(Pasting this extremely useful answer I found from D.J. Neary)
Typically, there is a material painted on the inside of the case back. There is usually a strip of metal or a very small spring that makes contact between the watch movement and the material on the case back. Sometimes, while changing the battery, the small spring will fall out or the material gets scraped off the case. Without good contact between the movement and the material your alarm will never sound.
D.J. Neary August 2006
DM, March 2008
