Why doesn't my camera's flash work anymore?

I mainly only use my camera to take pictures and the flash would work perfectly fine, but once I switched over to the video setting the flash stopped working.

When I first started taking video, the flash would not come on at all and after a couple attempts to get the flash working, I switched back over to Auto and the flash still won't turn on.

Before I switched over to video, the flash was working just as it should. I've had my camera for a while; do I need to replace the flash bulb?