My dad had a Jeep Cherokee as his take home car about 10 years ago, and it did the exact same thing once.... would not respond if you put it in drive, but if you started from "L", got some speed, and then switched it to drive, it would work fine.... I know those have an Aisin Transmission too, and if i remember, it was a relatively simple fix...
89' Toyota 4Runner SR5 V6 - 95' Lexus LS400
04' Lexus GX470 - 05' Toyota Corolla LE 5-speed
75' Cadillac Coupe DeVille 500ci