If you put the ring on the floor instead of on the BOTTOM of the toilet during installation, it could be out of place. Thus, the ring is partially blocking the drain.
One way to tell for sure if the problem is with your drain is to remove the toilet and fill a container that holds more than 6 gallons and pour it into the hole as quick as you can to see if the water rises. You'll have to pour pretty fast to simulate a flush. Have your shop vac handy (with the lint filter removed.)