If the solenoid is not clicking when you turn the key...it is not opening to allow fuel to enter the main jet...either there is no power to the solenoid when you turn the key...or you need a new solenoid...if you have a multi meter you can test to see if you are getting 12V to the solenoid when you turn the key to "on"...so if you are getting 12volts...the solenoid is bad...if you aren't getting 12 volts...trace the wire and see if it is either broken or rubbed bare and shorting out against some piece of metal on the tractor..or for a blown fuse in that line......in the meantime...if you have a fuel shut off on the tractor,,,take out the solenoid and cut the tip of the piston off ...now it is always open...so use the fuel shut off valve...turn it off and let the engine "run out of gas"... this is a temporary fix and you should get your hands on a replacement as soon as you can...good luck with it
Remove the solenoid from the bottom of the fuel bowl on the carb.
A wire should be attached to it, test for 12v on that wire when the key is turned "on". Do this first to insure the wire has 12v with the key on.
There is a small plunger, looks like a nail, sticking out of the solenoid.
Hold the solenoid against a good ground and turn the key on but not to start. The plunger should retract into the body of the solenoid while the key is on.
With the key off, it should pop back out, and be fully extended.
If any of this isn't working freely and fully, or if the sharp tip of the plunger is damaged, replace the solenoid.
If there isn't 12v on the wire with the switch on, then trace down where the fault is, and fix that first. No sense in buying other parts you may not need.