Hi there
I'm new here so don't kill me if this advice is not sound, when I picked up my Toro 12-38 Hxl mower I read up on a few bits of info to enable me to get it running again,from memory there is a process you have to follow to enable you to start it,I think you have have the p.t.o disengaged, handbrake on and maybe foot brake applied, you must be sitting on the seat as there is a cut out switch under the seat,I don't know if this information applies to your machine but maybe worth a go?
Kindest regards
Terry (the Limey)
P.s could be the solenoid ? Or bad wire connection!