If it's that noisey I'd say you don't need to diagnose it. You need to remove the chuck and take it apart, as that is the end result from finding anythig wrong anyway...
I'd simply plan to completely re-do it, as it's been my experience that trying to re-use any bearings results in more noise an dmore crap in the oil... If you're an aviation tech you can do the rear, but you need a rotating torque wrench if you don;t have one. Talk to Cass (Dr Diff) for any parts needs or help.