For a tranny to fail just like that — one time working and the next time not, at least in forward gears, tells me it’s an electronic problem. The first thing I would have checked is the solenoid pack.
Normally, the solenoid pack consists of a pair of solenoids. They are switched in and out to indicate which gear is being chosen. For instance, if the solenoid pair for first gear was solenoid one on and solenoid two off, then your 83 would be in first gear. Second might be solenoid one off and solenoid two on, while third might be solenoid one and two on, while fourth might be solenoid one and two off. Reverse would probably bypass them as it is a direct-linkage-type of gear, while a torque converter lockup for a slight overdrive gear would be the same solenoid pairing but with the gear selector in forward.
If the solenoids work — you check this by setting the parking brake and with the help of a friend you trust very well behind the wheel working through the gears and listening for the clicks — then it could be a sensor or pair of sensors.
Like solenoids, the transmission has been controlled by sensors and their settings since the early 1980s. So, let’s say the MAP (Manifold Air Pressure) sensoror the MAF (Mass Air-Flow) sensor failed, then it is quite possible the tranny won’t shift into the forward gears at all, while reverse may work quite well, just what you are talking about. And, if the TPS (Throttle Positioning Sensor) failed, then it is quite likely that you would lose the forward gering, as well, among other things.
With all of this said, the best thing you can do is find the proper OBD-II diagnostic scanner and software for your transmission and have a full diagnostic of the transmission run. Carefully note down all of the error codes and ask the technician running the test to give you a complete reading and printout. Don’t forget to check your list against the printout to make sure all of the error codes are listed. This is the only way to assure that you have the all of your bases covered.
I think that once you have the transmission diagnostic run, the primary error codes will be for the solenoids. The good news here is that the solenoids are fairly easy to access and swap out. They also go for about $275 per unit with labor or about $550 in total. This is a lot less than the $4,250 you would spend to put in a rebuilt transmission.