Having a similar problem with an old, old toilet (maybe 30 years old), I went so far yesterday as unbolting it and taking it to the back yard for closer inspection and testing. I didn't accomplish anything. I bought one of those cheap 25 foot augers from Kmart, which turned out to be useless. It wouldn't snake past the first bend in the toilet's internal plumbing. It's sort of like colonoscopy! The cheap auger cable seemed too limp to get past the curves. After removing the toilet, I tried dumping large amounts of water down the sewer pipe -- even used a garden hose full pressure -- and there is no clog whatsoever in the sewage plumbing. It's definitely inside the toilet. Out in the yard, when I filled the toilet bowl and tank and tried to flush it the same thing happened -- it just didn't want to empty. I knew nothing about the "jet" at the bottom of the bowl that you fellas are talking about. I'll bet that's it! I will have to put on my moon suit again and give it another try. Thanks!

You should have read my earlier reply. But I'll post it again.
I have one that most repair plumbers miss.. Look down at the bottom of the bowl. If there is a small hole, then that is a jet that starts the syphon action. If it's clogged the water will just swirl around and slowly go down leaving solids behind. Take your finger,(UGH! ) and run it around the inside of the opening. Over the years minerals build up and cut down on the syphon (flush) action. If it is rough or you feel build up, take a table knife and put a bend in it to get around the curve in the bowl and chip and scrap it clear. Next take a coathanger and clear out the holes around the rim. They start the swirling action. And last, check the water level in the tank. It should be 1/2" below the top of the over flow tube. And speaking of the overflow tube, Make sure the small 1/8" tube from the ballcock to the white overflow tube is connected so it discharges in it and that it's flowing when the ballcock fills. This is what raises the water level in the bowl. For a good solid flush they all have to work together. Hope this helps and thank you for rating my reply.. Tom