[tkwetzel]

Here goes some of my hard-earned (and expensive) education (I took two transmission classes last semester):

Tristan has given the best and most complete answer so far. Clutch packs are used to lock planetary gears which control the output ratio and rotational direction of the tranny. There are also bands in the transmission that have more control than the clutch packs (there are usually 3-4 bands and 1-2 clutch packs in a 3 or 4 speed automatic). The bands wrap around a large drum that is connected to part of the planetary set. The bands are tightened to lock a certain drum and therefore lock a certain gear in the planetary.

I would highly doubt that the gears in a automatic sheered off. The bands and clutches should slip before the integrity of a gear is compromised. And there is not much room inside the tranny, especially where the planetaries are, so if one tooth breaks, it doesn't have room to move and would affect the other teeth greatly.

There is no reverse gear in an automatic transmission. Reverse is achieved by locking one of the planetaries in a way such that it reverses the direction of rotation (usually locking a sun gear). The movement is transferred through multiple planetaries in most automatic transmissions until it reaches the higher gears. The same planetary set used for reverse would also be used for first gear and would affect the driving accordingly.

From what was described, I would guess that your problem is in the differential and not the transmission, but it could be either. The differential on FWD cars is technically part of the transmission, but acts separately.

If anything I said didn't make sense, feel free to ask questions.