The 3000 series were the Garden tractor version of the 2000 series and usually came with a hydraulic pump for deck lift, power steering and powering the attachments, earth augers, trenchers, rotary hoes , snow blowers, snow blade etc etc etc.
built from 2000 to 2005
You will find your repair manuals & parts books here
http://www.mymowerparts.com/pdf/Cub-Cadet-Service-and-Repair-Manuals/
The gearbox stand alone is also in the general manual .
I have only had one case like this and it was the input pinion that drives the diff off the tranny,'
Note the tranny & the diff are 2 different items ,'There is a cone shaped gear that wears.
I will also hazard a guess that the axel bearings in the diff are also cactus and the shift fork is worn thin.
I think I ended up replacing all axel bearings ( 4 of them ) the input pinion, and associated thrust washers along with the shifter fork and thrust washers here as well.
Not sure if all needed replacing but it was a very big job to get into the tranny so I opted on the safe side & replace everything that looked worn.
Must have worked because after he recovered from the heart attack when he got the bill, I have not heard a peep from his since and his 3 acres of garden are worked regularly and the same area of lawns seem to be nicely mowed.