Claire, if you want an "auto mode" but don't want to use flash, you can use Program mode (P) - and it should also adjust your ISO and exposure to get the shot, but you will to pay attention to the shutter speed in lower light to make sure you won't get blur due to camera shake during a longish exposure, especially if you are not using external camera support.
If you WANT flash in Program, just pop it up, it should fire when popped up. It should flash "HI" when it detects overexposure.
(As I understand auto mode, it will determing exposure and will use flash whenever it feels light levels are too low for handholding. Not sure why you are not getting it (the flash) to work in Auto mode.)
(When you have a chance, you might consider resetting to factory and see if that clears it up.)