I have a toilet on the second floor of my house whose bowl will not completely drain when it is flushed. The water runs in and out, but the level of the water in the bowl stays about the same even during the flush. In other words, I don't get a "clean" flush.

What could be the problem?

The chances are good theat your toilet itself is clogged. The obstruction is preventing the water from draining at the volume that is required. You can try a plunger, but, you are probably going to have to remove the toilet and look inside the drain area for the obstruction (now you know why plumbers charge the amount they do). Also look into the main drain area. If you have children they are usually the main source of this problem.
Have alot of fun!!!!!

Had this problem myself.Come to find out that the self cleaning bleach tablet got ****ed down tank outlet and jammed inside the toilet trap.
Those tabs take up to 2 months to dissolve
yea never know