Why won't my Yard Machine riding mower start?

Does the starter engage but the engine won't fire? Or does it just click when you turn the key? Or does it do nothing at all?

If it's the first option, it could be any number of things - bad gas, clogged carburator or fuel filter, bad spark plugs or wires, etc. If it's the second option (and you say you've ruled out a bad battery), perhaps a faulty starter or corroded wiring. In the third case, there are lots of ways the wiring could fail to prevent anything from happening when you turn the key, but the most likely thing would be a faulty interlock switch. Most riding mowers have various interlock switches (a.k.a. safety switches)which won't allow the motor to start (or in some cases run at all) unless they're engaged or disengaged. There may be one under the seat to make sure you're sitting on the mower (often in combination with one which detects whether the mowing blade is engaged). If your mower has a clutch/brake there's often an interlock switch on that to prevent you from starting the mower without pressing that pedal. Your mower may have others as well. It's usually pretty straightforward to bypass the various interlock switches if necessary to diagnose the problem (or to use the mower without its intended safety features if you're so inclined).