If you have the larger pumps, where each pump is secured with four screws (that aren't shared with neighboring pumps) then you can remove the pump and look to see if the internal spring is returning the plunger to the rest position. I've never seen a broken spring there, but it's possible. You should first remove the cover and observe the adjacent pumps for any difference in operation. The large flanged body pumps can be easily disassembled, but reassembly needs to be correct.
In both systems, there is a spring return, one difference is where the spring is located. If a spring is broken, then the pump plunger could be up, but still turning, so the rack will be free.
If this unit ever had water in the housing, rust could cause a broke spring, or a stuck lifter. Or in a bad case the roller tip on the lifter is bad or the injection cam is shot on that lobe, or both
Pics are still welcome for more informed diagnosis
Thank you. That is exactly what I needed to know.