Talk about bad timing. After a day of driving all over, I shifted into drive, tapped the gas, and the engine revved and it would not move at all. I put it into first or second (can't remember which), the transmission started shaking, but then it began limping enough to be drivable.

Fluid seems full (can't tell the color in the dark). No codes, it seems. Is this just a common solenoid failure, or is it really cooked? Original transmission, 186,000 miles.

Did you check for codes, or are you going by the CEL? Many transmission codes will not set off the CEL.

Nope, my scanner reported no codes at all. When you put it into drive, the RPM'* take about 3-5 seconds to change, but the car will still not move in D; only in 1, 2, and a little bit in 3.

The fluid smells okay, but it turned brown very quickly. There'* also a constant whining while it'* driven.

Brown means the fluid is burnt and from the sound of it, its metal-metal clutch packs. Sorry to say, its time for a rebuild.

If you pull the pan and there isn't any glitter you might just have a bad pressure control solenoid. Too bad to replace the solenoid you darn near need to remove the transmission to get the side cover off to service the electronics. I would check the line pressure and go from there.

Most home scanners wont read body codes or transmission.
I am not sure Colin what scanner u have but u may have to take it to someone that has a pro or shop scanner that can do a complete read of pending or stored codes.