Hello!
I don't know this projector in detail so I can't help you with a specific hint, but I may help with a more general approach.
I think there is a discharge lamp in the projector. Some projectors have bulbs with a wire, but most of them use discharge lamps. These discharge lamps have an ignition voltage of several kV, could be around 5 to 10 kV, sometimes even more. When the arc is ignited, the voltage is reduced to several tens of Volt, around 60 to 200 depending on lamp type and power, with a current between about a few hundred mA to a few A, also depending on power of the lamp. The voltage applied to the lamp is typically AC, not DC.
If the inverter is damaged no ignition voltage is generated, therefore the lamp won't be lit. If you have the proper tools you can check if the ignition voltage is generated.
But be aware of the fact that several kV can be present at the lamp!! Touching the voltage can be lethal!!!
So you need the proper voltmeter to measure a voltage in the area of 20 kV at least to test if the ignition voltage is applied at all. If it is present, and the lamp won't be ignited probably the lamp is damaged or burned out. If the ignition voltage is not present then the electronics is bad, could be a deaf capacitor (mainly electrolytic cap) or a melted down transformer. In case the transformer is broken there is only little chance to get the unit working again unless you can use a transformer from a broken unit with another failure. These transformers are usually custom devices.
Again: check what you are doing, the voltage generated will be hazardous!!
Also be warned that the UHP lamps have a pressure inside up to 200 bar or even more, so when playing around with the lamp wear safety glasses. This enhances the chance of waking up in the hospital with intact eyesight.
CU