Q: Reverse doesn't work

Hello. You can visually observe the manual shift lever on the transmission as an assistant puts it into reverse. You should see the lever move into position. The positions are all within detents so there is a positive stop feel. Reverse operates based on hydraulic pressures just as the forward gears do. If reverse is not functioning, something has malfunctioned internally (clutch pack, piston) and/or the required hydraulic pressure is bleeding off due to a blown or missing seal or o-ring. You could also have a valve body defect in the transmission.

The best thing to do is perform a pressure test and see if that yields an obvious clue (it should, but pressures are sometimes measured as part of a stall test, so this is not a DIY procedure). YourMechanic would be pleased to give you an on-site diagnosis of the shifting issue from which you will have at least an idea of the range of the cost to repair. You have a fairly common transmission, though, that can be rebuilt for less than $2,000 assuming no damage to the internal hard parts. Even an off the shelf already rebuilt unit is less than $2,000 plus labor to install of course. But, again, you should first diagnose what you have to be sure of the issue.