It turned out to be a gunked up starter. A local rebuilder cleaned it out for $10, believe it or not. For new starters, I have read that the Arco company of Pensacola, FL is a reliable source at reasonable prices -- arcomarine.com. It will even sell you starter rebuild kits for $25 in my case. Buying individual pieces would have cost me about three times as much.
Typically the only thing you need to rebuild on the starter is new brushes. On some mercs the brushes are hard wired to the end cap which is a good thing because it comes with a new bushing. If the gunk was on the bendix you should be okay. If they actually took it apart and filed the brushes and cleaned up the carbon dust your starter days are numbered. It could give you good service for a couple more years or a couple of weeks.