Yes, the worn plates could cause this problem. The clutch plates are very sensitive to the width of the plates, and as the plates wear the clutch pack(all of the plates) get thinner which causes the inner hub not to fully ingage(or in your case not at all) with the outer basket. You said that on some of the friction plates all of the material was gone, so that means it had to go some ware and most likley be the tranmission so your best bet is to tear it down, inspect the transmission components and replace the clutch pack and whatever else that needs to be.
hope that helps