The flash might just be turned off. To turn it back on, open the shooting menu by pressing the left side of the arrow pad. Scroll up or down with the arrow pad to select the flash option (indicated by a lightning bolt with an arrow at its end). Use the left and right sides of the arrow pad to select any of the options listed except for Flash Off.
If that doesn't solve your problem, please see the [[Olympus VR-350 Troubleshooting|troubleshooting page]] for more information.