My WAG: sharp angle + old low fluid = overheating.
like Kim said: you'll know how badly the transmission is shot by the amount of sludge (aluminized fluid) in the bottom of the pan...it will be a grey paste, and not red like normal ATF. It's caused be overheating...and when that happens, put money on the overheating causing other issues, like fried clutch plates and bands.
If you have the sludge, the transmission is useless (believe me, if it's in the pan, then it's everywhere). You'll either have to replace or rebuild.
Rebuilding is a pain, but definitely doable with the right tools and patience. Couple things:
- I'm betting it's a C5 (11 bolts on the pan)
- Is your '83 4x4? If so make sure you get the right filter (deep pick-up)
- Not 100% sure, but I believe the torque converter has no drain plug (for either the C3 or C5)
- If the ATF aluminized, you'll need a new torque converter because with no drain plug, you'll never be able to flush out the sludge.
Hope this helps and I hope the damage isn't too bad...
EDIT: and never mind about the 4x4 question...I see the answer now in your signature line