air conditioning fan works only intermittenly on 2003 Cadillac DeVille DTS

Why does air conditioning fan work intermittenly? IT comes on when right door slams or when going across a rough railroad track

Asked by for the 2003 Cadillac DeVille DTS
The blower motor brushes are worn and the slamming door causes them to make contact, at least temporarily. Just been through this exact scenario.