If a 15-year-old car (1993 Ford Probe Automatic 4 Cylinder) does not work in reverse gear (doesn't go at all in Reverse), the neutral gear works as the drive gear, and the drive gear works fine; What would be the problem? Can it be something else besides needing a new/rebuilt transmission? Thanks.

It most likely ia you need a new/rebuilt tranny.
One time it was in my linkage in the steering column though.