There are two sources of light, the model lamp, and the flash tube. The red power switch turns the whole unit on, and that should stay in the ON position until you turn it off.
The white ON button is for the model lamp only. If the model lamp does not come on, then the bulb may not be present (it screws into the socket), or the bulb may be a bad bulb (like any lightbulb can be). These bulbs can be swapped with any other household bulb (except CFL bulbs) so ensure the socket is working.
Also, be sure nothing is in the REMOTE jack on the light.