There are two ways for an RV toilet to fail. First, water won't enter the bowl when the foot pedal is depressed, so waste is not washed away. Second, water enters the bowl, but does not exit. Both issues are symptomatic of larger problems and rectifying them can be time consuming and unpleasant.
Water is Not Entering the Bowl
RV toilets work differently from household toilets; they do not use a cistern to store a reservoir of water that collapses through the bowl under its own weight. They use pressurized water -- either pressurized by the utility supplier through a connection hose or by a 12-volt pump -- that is injected around the top of the bowl, usually through several ports, which swirls around as gravity pulls it downward. This injection is controlled by a device called a vacuum breaker.
Check That Water is Pressurized to the Toilet
If water is not entering the bowl check pressurized water exists at the upstream side of the vacuum breaker by cracking the nut that attaches the flexible inlet hose to it; use a crescent wrench and turn the nut slightly counterclockwise. If water starts to bead around the thread, then the pressure is fine and the vacuum breaker must be replaced. If the hose can be removed with no water pouring out, then there is a blockage or turned-off stop tap somewhere in the plumbing system.
Water is Not Leaving the Bowl
Confirm that the black water tank is not full. Sensors and gauges fail, so it may be that the RV's central instrument cluster is suggesting that the tank is not full even when it is. Observe all the usual proprieties when emptying the tank -- do so at an approved dump station, wear protective gloves and connect the sewer hose securely -- then open the dump valve. If nothing emerges then close the valve, remove the sewer hose and open the valve again extremely slowly. If it fully opens and nothing can be seen to be blocking the exit pipe, insert a garden hose and run water into the black water tank to confirm it is empty.
If the valve opens and a blockage can be seen in the pipe or at the top of the pipe where it is attached to the black water tank, the blockage must be removed. A blocked pipe or tank can be cleared with chemicals available from RV dealers; empty the chemical into the tank, let it work for 48 hours -- driving the RV if possible to wash the tank contents around -- then empty the tank and flush it until the water coming out is pure. Do not use household bleach; it can corrode seals and damage in-tank sensors.
Determining if the Slide Valve is Stuck or Broken
If the tank proves to be empty but water is not leaving the bowl, the next check is to determine if the slide valve at the base of the bowl is not functioning. If so, it may be because it is seized closed or the actuating mechanism is broken. Turn the water supply off -- by disconnecting the connection hose and by checking the 12-volt pump is off -- then step on the flush pedal. If the pedal resists movement, the slide valve is seized in its closed position. Obtain the proprietary chemical noted above, empty it into the toilet bowl and follow the instructions on the packaging. If the pedal moves freely but the slide valve remains closed, the actuating mechanism is broken. It is necessary to remove the toilet to replace the broken mechanism.
If the slide valve opens, and the black water tank has been determined to be empty, but waste in the toilet bowl does not flush away, then there is a blockage in the pipe beneath the toilet that leads into the black water tank. Wedge the flush pedal down so that the slide valve is held open, then use a straight rod to loosen the blockage. Follow this with a bucket of water to flush the loosened blockage away.