Exactly what he said. There's a big switch attached to the side of your transmission between the selector lever and the transmission. Your computer uses it to tell what gear you have selected. The switch sits right beside an exhaust pipe, which probably helps it die. When it dies, it gives scratchy readings to the computer, like an old stereo volume knob.
The computer is actually smart enough to know that something is going wrong -- if it detects a bad signal for five seconds, it will go into a limp-home mode. It will assume you're in D, and adjust the settings on the transmission so that they are REALLY hard. Charmingly, it does NOT light any other warning lights.
Turning the car off and back on resets the computer until the next time it gets a scratchy signal. This scratchy signal is also what the computer uses to light up the selection display in the instrument cluster. This is why he said to look for them to flicker. In my case, it would bounce around from R to L for a while, then finally settle down to D.
Swinging the shift lever a couple times *might* clean the contacts enough to get you by, but you should probably replace the switch ASAP. Other users have recommended some exhaust shielding tape to protect the switch.