I have plunged and augered the toilet. I have cleaned the holes under the rim. There is not another hole near the drain. When I flush the toilet, it swirls well but the water rises slightly and then slowly drains with a slight swirling action.

You don't have a small jet hole in your bowl? Then you have a gravity toilet that flushes by the weight of the water entering the bowl from the tank. How high is the water level in the tank? It should be 1/2" below the top of the white overflow tube. You need more water to start the siphon action. Good luck, Tom