Hi, Logmanup (slight bouts with dyslexia, sorry)
By "spinning water dispensers", I assume you mean the spray arms, right? OK... if they are getting clogged with debris it would be nice to know what kind of debris. Pieces of broken glass? Plastic? Lime scale? Iron? And yes, when they get clogged they won't rotate, won't allow pressurized water through and therefore won't clean the dishes.
For the purpose of this solution, I'll assume that there are little white particles clogging up the jets on the spray arms. This indicates hard water and lime scale build up.
Other than completely disassembling the entire motor/pump assy. (you really don't want to go there), the best way to clear this out of the system is to use an over the counter chemical called Dishwasher Magic
or something similar. If the lime scale build up is really bad (and it sounds like it is), use a couple of bottles to start with and follow up with a bottle per month thereafter.
As an aside... If I assumed correctly about the lime scale build up, that means that it's also affecting other appliances as well. Mainly, your hot water heater. If you haven't done it before, please read this
to perform maintenance on it. And a product something like this
for your washing machine.
I hope this was helpful. Let us know if this works or not. If not, please write back and we'll go a little deeper.