Won't start up. (by 2 users)

Hi, having problems wih my (usually) wonderful camera. The camera won't start up, I've tried two different sets of new batteries that have worked perfectly when tested elsewhere. Sometimes, if I take out the memory card and the batteries and then put them back in, when I press the power button the screen flashes for a second before turning off again.

The problem started when I took the batteries out without first turning the camera off, leaving the zoom sticking out. The zoom hasn't retreated back into position since, and anything I try to get the camera to start up so that I CAN get the zoom back into place hasn't worked. Any help would be seriously appreciated.