Find the fuse and replace it
Remove the blower housing, remove the kill wire on the coil and spin the motor while checking foe a spark
if you get one with the wire removed ans don't get one with the wire attached ( Parking brake on & Blades off ) then you have a safety circuit problem .
Check the trigger wire at the starting solenoid.
With the parking brake on & Blades off you should get battery voltage on the trigger wire with the key in the S position.
I would have loved to have told you where these bits are and what colour the wires are but there are 142 variations of a Troy-bilt that could have been fitted with a 42" deck and no one but you knows which one you have