Firstly have you got the manual ?
Secondly what most people have trouble getting their heads around is with the exception of the cranking & PTO circuits, all of the rest are ground wires .
As such there is no connection between the kill functions doing funny things & the mower failing to crank
You mentioned the solenoid, did you replace it and if so did you connect the small red wire to the powered side of the solenoid and not the switched side ( we have all done it at least once ) .
Other than that it is out with the meter / test lamp and hang from the rafters trying to get to the switches .
The manual tells you how & where to test and what the results for each test should be .
BAsically the cranking circuit is a daisy chain from that power feed wire on the top of the solenoid, through the key switch , through the PTO switch , through the brake switch then down to the trigger terminal on the solenoid .
The last item, brake switch is some times hooked up to a relay switching the power and the lap bars connected to the ground on the same relay or a second relay and these feed the power to the starting solenoid trigger terminal.