Why does the blower/fan for heater and air conditioner work sporadically?

What is your question?

Car only has 45,000 miles, have had this problem for a year. Dealer said it needs a new motor ($600) not covered by warranty. If it's the motor then why does it work about half the time. I've discovered that when it refuses to work, if I open and shut the glove compartment with a little force, it will sometimes work. What's up with that? Electrical problem?