how would the rock cycle be different if the water cycle did not function?

Answer 1

If there was no water cycle, the rock cycle would only have 2 parts, igneous and metamorphic.... sedimentary rocks wouldn't exist, and metamorphic rocks would be considerably rarer than they are.

Answer 2

Think about it. The rock cycle would become near static. The only erosion forces would be wind.

There would be no freeze thaw mechanical fracture, there would be no water transport and there would be no chemical (oxidation) processes.

The only significant input into the cycle would be volcanic.