They rarely fail, and many don't know how it works.
The prime start system does nothing when you push the key in or pull the "choke" lever on the control box.
The way it works: the plastic white colored plunger mechanism has a type of wax inside of it. At cold air temps, the plunger is drawn up into the body, which uncovers a couple passages (one for air one for fuel). Once the engine is started, the alternator (or generator) supplies AC voltage to the two wires on the prime starter which warms the wax inside of it, and as it warms, the plunger drops down to cover the two passages.
One can test the primer mechanism by removing it from the carb and throwing it into the freezer for a while. Measure how far the plunger is up inside of the body. Let it warm up a while to room temp and see if the plunger drops. If it does, it's working--and I suspect that it probably is since I have never once seen one fail. BUT what I have seen VERY often is the passages in the carb(s) get plugged, which then causes all sorts of problems that people blame on the prime start mechanism. I know, most say well I've had the carbs apart and they're clean as a whistle....but on some of the carbs you can't get to the passageways that feed the prime start's fuel; they are close to impossible to access, and to actually get to them requires drilling out a plug in the bowl, then tapping it for a screw/plug. No fun.
On C90, I don't remember "exactly" how your particular motor is set up. Some have electric choke, which is an electric solenoid that kicks all 3 choke plates shut when you push the key in or pull up on the choke lever at the control box. Then they changed it at one point to use true prime start, which works as I described above, it's got a red lever on one carb that you can use to manually "choke" it-to get it started. Later ones didn't even have that. On prime start motors, you do not advance the throttle to start a cold engine, nor do you use the push to choke or pull lever up to choke as they do no good. Advancing the throttle on cold stat makes it even harder to start because there ain't no choke, so you're just adding more air, which makes it even harder to start. No throttle, crank until it starts--assuming the fuel passage(s) are clear.
The prime start has been a source of many frustrations from owners to techs; and once the system's operation is learned, it then becomes almost EFI-like in cold starting. I've known techs to give up on them and tell the owner to sell it and/or try to buy it from the owner.