Do you have a wiring diagram for the tractor? Is your tractor a geared tractor or shuttle shift type? A couple of switches I can think of are:
1) Safety switch under the tractor seat - if you are not sitting down, thw switch cuts out the engine when running. To start you have to be seated.
2) If a geared tractor there will probably be a clutch switch - these are often out of adjustment. To start the engine you need to have the clutch pedal depressed (so it won't start in gear - much like a car) or the engine won't start.
3) If some sort of shuttle, there maybe a switch involved with that - don't know as I have never used one.
Any of these switches can be jumped or bypassed to get the engine running.
are any of these likely candidates ?
HTH