Make sure that the ring flash is switched on - the flash on/off switch should be pushed up so it meets the yellow lightning flash symbol.
If the flash still won’t fire, then the camera may be conserving battery life in low power mode. You can check if this is the case by looking at the red power indicator LED - if the camera is on and it is blinking, the flash will be inhibited in order to conserve battery, and the camera needs to be charged.
You can also check how much battery life is left by counting how many LEDs in the ring flash light up when you press the shutter button while the camera is switched off. If three or fewer LEDs light up, then there is not enough power for the flash to fire and you should recharge the camera with the USB charging cable provided.