It took me a while to track down the problem. Lots of other people seem to be having it also. In the end I discovered the problem was caused by a telephone marketer and poor default settings on the Blocking Mode.
The Galaxy S3 makes it easy to block unwanted telemarketing calls and when my wife got one she immediately added it to the offered 'Blocking Mode'. Blocking mode was started and that's when her alarm problem began. She didn't notice it but she wasn't hearing incoming calls either!
It's easy to fix. From your home screen swipe down from the top right hand corner of the screen. You'll see at the top under 'Ongoing' Blocking mode. Tap it and remove the check mark from 'Disable alarm and timer' then go down the screen and turn 'Allowed contacts' to 'All contacts'. Had you noticed that your phone was not playing ringtones?
