I'd start with the bulb, unless there is a smokey aroma coming from the transformer. You should change your grow lights out every year anyway, since the degrade some after long periods of use. They still light, just not as intense, and you want maximum yield and quality.
Anyway, don't know too much about these, so may not be entirely correct. These are a form of arc lighting, high voltage. So caution is a good idea when messing around. It will flash, when the potential is great enough to jump, but the gap is too worn to sustain a continuous arc. Pretty sure there is much you can do if the transformer is fried, the capacitor would be pretty obvious if failed. Not sure of your fixture, but likely cost about the same to replace the transformer, as buy a new fixture. Bulb would be cheap in comparison. I was given two fixtures years ago, no bulbs or documentation, so they still sit in a box some place. No way of knowing if they are mercury or sodium, or if they even work. Wired up with orange extension cord (was going to salvage), and an extra grounding wire.