When putting shift lever into reverse nothing happens

Sounds like something is loose and shifting position in the gear shift linkage. Block the wheels for safety, then crawl underneath and watch the linkage and brackets while a helper moves the shift lever. Look for a mounting bracket that moves around. Also watch the shaft that pivots in one of those brackets. There is usually a nylon insert in the bracket that the shaft goes through. If that insert cracked apart, the shaft will shift position instead of being forced to turn when you move the shift lever.

Look at the lever attached to the shaft coming out of the transmission. That little shaft is where the "click" comes from when you shift gears. If you see the linkage rotate without hearing the accompanying click, that part might be loose. That is easier to see when your helper moves the shift lever back and forth repeatedly between two adjacent gears, like "D" and neutral, or "2" and "3".