Chosen Solution
The built-in flash on the camera will not flash no matter what the setting. The display reads that it is BUSY each time the shutter releases but no flash. I can hear a little click sound in the flash area when it supposed to flash but no actual flash.
Do you have a plastic cover placed in the hot-shoe slot? I had the same problem and that is what was causing it.
The camera ships with no hot-shoe cover, I decided to put a spare one on there to keep it clean and the realised the flash wouldn’t raise, removing it fixed the problem. It must be a feature designed to stop the flash from raising when there is a speed-light attached.