Kubota M8540HDC, L5740HSTC, BX2200, BX2660, John Deere 425&1025R, Case, Massey Ferguson, Ford
Have you checked the linkage? Is it turning and powering an implement? The reason I ask is that on some tractors the rear PTO shaft will rotate slowly even when not engaged, but have no power.
The PTO lever operates a cable that goes to the transmission to engage/disengage the PTO. When my L4610 was new, the lever at the transmission end of the cable kept slipping so the PTO would not disengage... just like yours. Dealer repaired it at no cost and it has been trouble free ever since. Your L3400 is probably similar... you should be able to see the linkage from underneath.