There are several possibilities
Here are the easy ones:
Is the seacock open?
Could the thru-hull be blocked?
Could the holes in the bowl rim be calcified (blocked)?
Has the unit been modified to flush with freshwater from the holding tank?
How does the pump behave in each position?
Does it carry waste away in the "pump dry" position?
Do you encounter a lot of resistance in the "wet bowl" position?
Others my think of more things to check, but my guess is that if it isnt one of the above and you arent getting a lot of resistance to pumping in the wet bowl position, there are blown seals/flaps in the pump assembly.
For inexpensive manual toilets, it's often more cost effective to replace it than to try and rebuild it.