Make sure the battery you are using is charged; attempt to recharge the battery if necessary.
The charging indicator may flash if the battery has not been charged for a long time or if it is new, right out of the box. In this case, temporarily remove the battery and try charging it again.
If the charging indicator does not light up or blink while charging, make sure the metal contacts are free of any foreign material that may prevent charging. Use a dry cloth to wipe away any dust or other material on the battery terminals.
I also recommend checking this link for additional troubleshooting steps if the camera will not turn on.
If the issue is still unresolved, service may be required. Send your camera to a Sony facility to be repaired.