89 corolla sedan.
I had the same problem. differential seals- where the driveshafts go in- had been leaking.
This is truly the achilles heal of an otherwise awesome vehicle.
If you have a Corolla it will be well worth your time to replace the seals.
Most owners don't know to check the fluid level in the differential. I didn't.
The differential hub gears were badly worn. Shavings in the gear box !
I live in Kapaa, HI and could not find a used tranny so had to rebuild.
The parts were $500 with shipping!
It is not hard to swap trannys in this car. Just time consuming. It took me about 8 hours overall, including
replacing driveshafts, ball joints and tie rod ends and struts.
I still have a whining noise though and wondered if anyone out there might know what this is.
I am at a loss as to why it would be making noise after the rebuild.
It surprised me that Toyota uses atf fluid in the gearbox.
If anyone has questions on how to replace a tranny you can contact me at firstname.lastname@example.org
If any has an idea what this whining sound is please contact me as well.