Transmission

First thing would be to look at the fluid and see if it is good. It should be red to a light brown and clean, If it is dark brown to black you will need to have the trans torn down for burnt clutch packs and bands.
If the fluid looks okay then it is likely the reverse servo has failed and the reverse band is not applying. The servo can be tested and replaced without removing the transmission, but it is not a DIY type of job. I would suggest taking it to a shop you trust. They can test it and give you a hands on answer.