the heater blower motor on our 2004 grand prix will sometimes stop, and then will start up again(usually right away). its been doing for about a year
Next time the blower motor stops working, reach under the passenger side of the dash and tap on the blower motor with the handle of a screwdriver. If the blower starts working the blower motor requires replacement.
A common issue with the Grand Prix is water leaking in through the gasket by the hood hinge area when it rains. Do you get wet floor mats with heavy rain? The water leaks in on the passenger side right over the blower motor resistor, causing it to short. It’s a $10 part. But, it is hard to get at; behind the ac and up against the firewall.
I had that precise problem once but in an Escort. The connector was just corroded - unfortunately the leak wasn’t bad enough to be noticeable on the floor. So I’d start by just pulling and cleaning the connector.