And exactly how you measure humidity doesn't explain the basic fact
that the problem humidistat is not responding at all. The OP clearly
stated that he set it just short of the point that would make it come
on immeadiately. In a house where it's cold enough outside that the
heating system is running frequently, the humidifier should then come
on soon thereafter and start running occasionally to keep the humidity
up. His humidistat only turns it either on continuosly or off,
depending on where he sets it. Definitely sounds like it's failed and
simple to replace.