Low on transmission fluid, and overheated, perhaps? Now, it's cooled, and everything has relaxed enough to allow it some movement. Although, getting it back up to any speed would almost certainly lock it up again.
Check replacement (used/rebuilt) transmission costs. In future, include this vehicle in the "severe" column when it comes to maintenance. Use the time tables listed, instead of the mileage tables.
Was that fluid on the ground red, perchance? Probably brown, actually. Was the transmission fluid ever changed, or checked? You said you checked "obvious fluids", but not specifically which those were.
Best of luck,