Why does the heat blower not work on a 2003 Monte Carlo when you first start up but will work after the car runs for a while?

The engine should begin producing heater output within the first minute. Might take a little longer in colder climates. Although it sounds like I may not be warming my car up before turning on the heat blower, this never happened until a month ago. Even if there is no heat, shouldn't it at least blow cold air? Nothing blows....what could it be? If the BLOWER(FAN) is not blowing no mater what speed or settings are used on the climate control center(AC,DEFROST), the the motor itself is bad. A good test is to take a ruber malet and lightly smack the motor directly with the engine running. If the motor suddenly starts blowing then the motor is bad. About $110.00 to replace with common hand tools.