This just happened to me too. It's definitely the water softener. We bypassed it and got water to one bathtub in one bathroom; the rest of the house is without. Aside from going from pipe to pipe and re-doing the plumbing, does anyone know of a way to unclog the water pipes?

How large are the balls? Can you bypass the softener and flush the pipes out the faucets? In the meantime this might help.(see image) Good luck, Tom

Long shot here but sounds like you are in the market for a resin bead kit and a new screen. How to change the resin in a water softener.