Allainguillaume, there are a few possibilities. Check the capacitor, make sure it is not leaking or bulging. Check the flash unit itself to make sure that the light is working. There are two fuses on the Flash PCB, make sure that those are showing continuity with your multimeter. The flash unit replacement number is Vek0L84 and it is available at multiple places for around $20. Here are the instructions for the flash unit. Remember to discharge the flash capacitor.
1. Be sure to discharge the capacitor on FLASH PCB.
2. Be careful of the high voltage circuit on FLASH PCB when servicing.
1. Refer to the disassemble procedure and remove the necessary parts/unit.
2. Put the insulation tube onto the lead part of Resistor (ERG5SJ102:1kΩ /5W). (an equivalent type of resistor may be used.)
3. Put the resistor between both terminals of capacitor on FLASH PCB for approx. 5 seconds.
4. After discharging confirm that the capacitor voltage is lower than 10V using a voltmeter.
Hope this helps, good luck.