It is a bit of a learning curve, seeing as though there is so much room to work- but there are 2 drive belts and a dual pulley called a variator which will likely need attention. The pulley has a movable center that has to move freely. Also, be sure that the brake is not dragging severely. If you replace 1 drive belt, replace them both.

I have a John Deere RX75 that stopped working last fall. After further investigation, I realized one of the pulleys had seized. I took it apart and meant to order a new pulley, but the snow came. Now I have the new pulley, but can't remember how to get the thing back together. Could someone shoot a picture of the underside of their RX75 without the mower deck on so I can see how this thing fits together or pass me a manual that shows the drive pulley system. Thanks.

Could be one or more interlocks. My first choice would be the ignition switch (key). Sounds like intermittent contact. Second choice would be the solenoid. Do you know how to jump the solenoid? This would help you focus on whether either part is the culprit. To jump the solenoid, you need to put +12v to the third wire (the smaller connection). Solenoid should click and start cranking motor.

***"the carburetor is clean"*** Does that mean you have taken the carburetor apart and cleaned thoroughly or does that mean that the outside of the carb looks "clean"? To check whether the engine wants to run but is not "getting fuel" you can dribble a spoon or two of gasoline into the throat of the carb, or give it a shot of spray carb cleaner into the carb and see it it wants to run briefly on that amount of fuel. If it wants to run when you do that, your carb is not so clean (inside) after all.