Transmission will not shift into reverse after having the battery jumped?

I would check the fluid level first, here is how this transmission uses a see through eye to check the fluid level

Fluid Types

Updated by TSB 13-AT-011

Automatic Transmission Fluid Type

Type .................... SP4-M
Capacities

Automatic Transaxle Fluid

Capacity .................... 7.71 qt (7.3L)

This guide can help as well,

https://www.2carpros.com/articles/automatic-transmission-problems

If the fluid level is okay we should scan the car, you can get a CAN scanner (Controller Area Network) from Amazon for about $30.00 here is a video to show you how.

https://youtu.be/u-4syLc-ifQ

here is a scanner link

https://amzn.to/3o41KcZ

Check out the images (below). Please let us know what you find. We are interested to see what it is.