The contacts in the battery compartment may be dirty or corroded.
* Open the battery compartment, take the batteries out and check the condition of the contacts.
* A pencil eraser works well for cleaning contacts.
* If the contacts are clearly corroded, they may be cleaned with fine emery paper. Note however that heavy corrosion indicates that the old batteries have leaked acid, and this may have damaged the camera's electronics beyond the battery compartment. If this is the case, the camera won't work no matter what you try, and must be repaired.
* Put the batteries back in, observe correct polarity as noted on battery compartment.
If the camera still refuses to to work
* Make sure the batteries are indeed new, and fresh. New batteries that have been kept on the shelf for 5 years may no longer be usable.
* Use premium quality alkaline batteries only. Cheap flashlight batteries are not suitable.
* Beware of counterfeit (fake) batteries. These look exactly like premium quality batteries from well-known brands, but are of much inferior performance. They are widely sold at convenience stores and such. Make sure you buy your batteries from a reliable retailer.