The battery may not be charged enough to turn on the camera. Take out and charge the battery for 5 or more minutes and then put the battery back into the camera. The battery may also not work anymore or won't hold a charge, and in this case needs to be replaced.
The memory card may be switched to lock, causing the camera not to take any photos. Take out the memory card and switch the little piece to the "unlock position". The memory card may be unlocked but the camera still could not take pictures because the memory card may be faulty. Switch the little piece on the memory card to the "lock" position.
The flash may be turned off on the camera. Press the circular button surrounding the "FUNC. SET" button to the right turns the flash on and off. The bulb also may be burned out, causing the flash not to work. The flash bulb may be replaced but if the entire flash assembly has been damaged you will need to replace the entire flash assembly.