it sounds like the system was wired wrong, the feed wire
on the switch should kill power on the fuse block when
shut off, someone has put a constant hot feed to the block
bypassing the switch ,the only thing your switch is doing
it sounds like is sending the hot feed to your solenoid
to activate the starter . cut everything off on the
vehicle an take neg cable loose from battery if it is
arcing a little there is a closed circuit somewere.
the switch could be faulty ,i dont know what type of
steering column you have but if it is the rod type
that is exercised buy the switch, check an see if
actuator is going into full stroke to line up contacts.