The flash light of my HP Photosmart E427 digital camera stopped working. What is wrong and how do I solve it?

When I bought it, it automatically flashes when snapping in a dim or dark environment. About one month later, the flash was no more consistent the way it use to work before and now the flasher has stopped working completely even when the flash is set 'on'

This is most likely a malfunction of the camera/flash. Since you recently bought it, it should be still under warranty. I do not recommend trying to fix it yourself as this will void the warranty.