This is probably the single most commonly encountered error among compact and bridge digital cameras. It may indicate that your camera needs repair (or replacement). Before you go that route, however, there are several things you might try. These are not foolproof and they're not guaranteed: if your camera needs professional repair then it needs professional repair.
There are many causes for this. One is impact, caused by dropping the camera or knocking it against something, especially with the lens extended. Another is dirt or grit in the works, jamming it. Ironically, one of the most common sources for the dirt or grit is the camera case. Cases tend to accumulate dirt and lint and other stuff, which eventually get transferred to the camera. Another cause is the camera getting turned on while the lens is obstructed. This can happen if the camera gets turned on inadvertently while in its case or a purse or other confined space.
Cross your fingers and try these steps in order.
- Warranty: If your camera is still under warranty, take advantage of it.
- Power: If you have an AC power adapter for your camera, use it. This is not the same thing as a battery charger, but instead a device intended to power the camera for a long time on AC power. If your camera has a Lithium-ion battery pack, make sure it's fully charged. It your camera uses AA or AAA batteries and you're using rechargeables, put in a fresh set of alkalines instead. The purpose of this is to get the maximum power to the motor. Try turning on the camera.
- Air: Using a bulb-blower if you have one and a can of compressed air if you don't, try cleaning the area around the lens, where the segments normally extend. Be careful not to blow more grit into the works. Try turning on the camera.
- Orientation-1: Still using the power source from the previous step, place your camera on its back on a hard flat surface like a tabletop with the lens pointing straight up. Try turning on the camera.
- Orientation-2: If the previous step didn't work, turn the camera over so that the lens is down, and try turning on the camera. Sometimes the extra effort of lifting its own weight will jar it free.
- Jiggling: This is pretty much the last resort, but since your camera is out of warranty and nothing else works, so what do you have to lose? Jiggle the lens with a fingertip as you turn the camera on. Side-to-side, up-down, clockwise-counterclockwise. Don't push down on the lens so hard that you keep it from extending.