It's either mechanical or electrical. Open the back door, start the machine, unplug the fuel shutoff solenoid. If it's mechanically sound, the linkage will spring over to stop and she'll quit.
If it's electrical, figuring out what's wrong might take a little longer. G- or F- series? F-series, could have bad wiring anywhere between the keyswich, fuel shutoff solenoid and timer, sticky relay, etc., but the power to the solenoid is not shutting off when you trun the key.
G- series, if it's not the computer, you should get some kind of code in addition to the fault, whether the code is for the start circuit or not. I can think of some different scenarios.
F- or G- series?