Easy probblems... theres a huge leak under the transmission, and the reverse went out...

vast did H3LL millions for 70+ years.dead.
well wouldn't move under engine power you meant.
if fluid level drops way low , engine idle in park, tested that is bad.
now do know the trannyy oil pump can fail like that. and that makes all gear clutches and bands 100% DEAd AND IS NEUTRAL.
NO PUMP NO JOY ever. all is dead. and fake Neutral.
IN PARK THE PARKING PAWL KEY LOCK up THE BOX
TO MOVE CAR PUT SHIFTER IN :"N": and it moves

the foot brake is pressed to unlock the shifter from Park
or can not do that, or some cars key off does same.+N./
the users manual cover towing a car rules for sure, but you lost that as most do.
the TCC soleniod can not make any transmission go to false neutrals or FLAREs moving.

gee unplug it TCC relay and see for self . if is a relay there.

of PRNDL1
if all forward gears are bad and reverse the pump is dead or pump sucking dry pan.
or a U joint blew up to H3LL and gone as they can do.

the other causes, inside the box are
besides dead pump and its regulator
is leak in the pump main gallery feed any huge leak is just like a dead pump, and easy to happen via all those complex paths.
a 16 year run on any slush box is GREAT.

the car must move in L or R, or tranny is bad.
most times and not u-joint exploded. some junk iron ones do that easy buy them forged steel rated and win.

im assuming this is an automatic transmission? it sounds like the cable or the linkage to the transmission gave out. your gonna have to get under the hood or under the car to see. it may be a easy fix-good luck!

probaly a broken rear/lower planetary set or ring gear is broke

that most likely is your transmission fluid and you probably leaked out 4 to 5 liters , you must have a transmission line that has blown you will have to replace the leaking line and then add mercon 5 through the transmission dipstick the vehicle will have to be running to get an accurate reading keep in mind when you pour in fluid you have to wait about 1-3 mins before you can get an accurate reading due to fluid being inside the tube and when you pull the dipstick out it will read full, so pour in the fluid and the wait a bit start it and check it, the leak is most likely comming from a line.

There are at least 5 places on the Automatic transmission that can over time, and mileage develope fluid leaks. Front converter seal at the front of the transmission,pan gasket in the center,dipstick tube o ring at the center on one side ,speed sensor o ring,and the tail shaft seal at the rear,of the transmission.
Place a flat piece or huge card board,under the engine and transmission,after driving you will see where the fluid,red in color is dripping. Its easier to spot exactly where the leak is comming if you can look under the car,while it is running, The easiest leak is the pan gasket,the dipstick tube, and the speed sensor,then the rear housing tail shaft bushing and seal.
If the front seal(converter seal) is leaking the transmission will need removed,and the seal,and maybe even the front pump bushing Replaced,it would be a good idea to replace the bushing esp if it has high mileage,80,000 or 100,000 miles of use.Change the fluid and the filter,while repareing the leak or leaks.Is a good idea.

If you are talking about a automatic transmission your front band needs adjustment. If you are a do it yourself type, It's a matter of loosening a lock nut and backing out the adjusting screw and retorquing it to the proper in/lb..

There are two lines that run from the radiator to the transmission. Those are the cooling lines.Follow them carefully and you will find the one that's leaking. If the fluid is coming out under the car, between the trans bellhousing and engine, likely you also burned out the front pump seal. If so, don't bother replacing it without having the unit rebuilt, or replace the unit with one from a scrapyard. BUT if you were doing 100mph when the leak began, it is more than likely that you burned out the transmission. The parts in there are very sensitive to low fluid conditions and will quickly burn up the internal clutches if it is low (especially at that speed)
Sorry to have to tell you that but with transmissions, that's what happens and there aren't any easy cheap repairs.

check your transmission fluid.....if possible use a transmission additive to try and solve this....or top up with transmission fluid as required...check for leaks under your car of colored oil..usually red...you could have a leak and losing transmission fluid...if so top up with a sealant fluid for transmissions...this usually works for small leaks...you have to drive about 30kms to get the fluids to circulate...for the seal to work..

Try Putting Trans-X in it if it do not leak to bad. This will stop minor leaks, and adjust bands

You really probably shouldn't be driving this vehicle right now. If it is leaking transmission fluid, and will not go into reverse, it means there is not enough transmission fluid in the vehicle to perform that task. Check the fluid. If there is plenty of fluid inside and it will still not go into reverse, you are looking at a new transmission. Whenever you feel your vehicle try to slip gears as you go down the road, you need to take it in to be looked at immediately to prevent things like having to get a new transmission. You may not have a huge problem yet, they may be able to stop the leak, but if you continue to try and drive it, it will result in a new trans.