Su,
I wouldn't have thought it has a'starting motor' - they aren't THAT sophisticated. Sounds like that the fan shaft bearings are getting siezed up [due to age and the heat probably]- thus taking longer to "get going". It's a very hot environment and alien to fan bearings really.
All parts for Diplomats should be readily available - just use searches on this page. Best of luck.
Dave, November 2007