No powersteering and lift

Sounds like clutch/assembly is out- definitely need repair!

possible problem with gearbox

The question is a little vague but I think I know what your referring to. All modern automatic transmissions have torque converters. This is the device that connects the engine to the transmission. All vehicle manufacturers like the trans to be nice and smooth shifting. That's great but it does come with some minor drawbacks. If you are facing slightly down hill and you put your car in reverse but do not step on the gas slightly I can guarantee that you will indeed roll forward. You can eliminate that issue by holding your left foot on the brake while you shift into reverse. Then, as soon as you feel the trans engage, gently depress the gas pedal with your right foot and it will eliminate that forward roll problem.

It is an auto I take it and the problem will be a reverse band/clutch pack solenoid servo. It it is a manual then the clutch works the same way in forward and reverse so if it was slipping in reverse ,it would also be slipping in forward gears as well. Run the fault codes to check for TCM and servo/solenoid faults.

Does it crunch? If you lift the clutch and then press it down whilst trying to get it into reverse as this lets the cogs move allowing you to slip the drive into the gears this may allow you to get it into reverse. So here's the steps:
1 start the the engine
2 drive the car for about 10 kms
3 try and get the vehicle into reverse
4 lift the clutch whilst holding the stick in the gate ( you should feel the cogs turning and shaking the stick)
5 then push the clutch down again
6 if it still won't go repeat step 4/5
if it still won't work then try and get it into reverse whilst stationary and then start the engine it will jolt but can free up the gears!

hope this helps :)

Common problem probably a 4L60E transmission The low and reverse clutches are the same ones The forward clutches are another set and then there are the 3-4 clutches in another pack. So you probably burn out the forward clutches or could be a stuck valve in the valve body. Time for a transmission specialist.

When the engine is idling and the gear box selector is in Neutral all the internals of the gearbox are rotating. Pushing in the Clutch disconnects the drive from the engine to the gearbox but it takes a few seconds for the gears in the box to cease rotating. All the forward gears have synchromesh so there will be no crunching noise ifa forward gear is selected immediately the clutch is pushed in before allowing the gears to stop spinning. On the other hand Reverse has No synchros and therefore selecting reverse before waiting a few seconds for the gears to stop spinning will produce the crunching noise you have described.
So it pays to wait a second or two after pushing in clutch before Reverse is selected to minimise the crunch and if the clutch appears to be working correctly in normal driving ,then no adjustment is necessary.

It does sound like a clutch, but deserves to be more thouroughly checked out, Does the clutch pedal feel normal? is there a little free-travel at the top of the pedal stroke? do you see oil dripping under the car?
Clutches usually go out slowly, they start to slip under heavey load first, then gradually slip even under light loads in low gears. If an axle was loose, it could have spun in it's hub, with the hood open ans an observerstanding beside the car looking down at the axles, slowly let the clutch out (engine running, in reverse gear, ) being careful not to hit your assistant, if the axles turn- one of them, but the wheel doesn't this is your problem. If the axles don't turn with the clutch out, and engine still revs, well it's time for a clutch or transmission, Good luck, hoe this helps

4R100 or 4R70W?

Geartrain
Power is transmitted from the torque converter to the geartrain components through the input shaft and forward clutch cylinder.

• By holding or driving certain members of the gearset, four forward ratios and one reverse ratio are obtained and transmitted to the output shaft. The ratios are as follows:

GEAR RATIO 1ST 2.71 to 1 2ND 1.54 to 1 3RD 1.00 to 1 4TH 0.71 to 1 REVERSE 2.18 to 1
Input Shaft
The input shaft is supported by two bushings in the stator support. End positioning of the input shaft is controlled by the splines in the converter turbine and the overdrive planet assembly.
Output Shaft
The output shaft is supported by two bushings in the case and by the slip-yoke and bushing in the extension housing. End positioning is controlled by the parking pawl gear and snap ring or shoulder and by the reverse ring gear hub and snap ring.
Overdrive System
The overdrive planetary system consists of the overdrive planet assembly, overdrive sun gear, overdrive ring gear, coast clutch cylinder, overdrive one-way clutch assembly and the center shaft, as shown in the following illustration. The overdrive planet assembly is splined to the input shaft. The overdrive sun gear is centered by a bushing on the input shaft and held in place laterally by needle bearings on the reactor support and the overdrive planet assembly. The overdrive sun gear is splined to the coast clutch cylinder, which in turn is splined to the overdrive one-way clutch inner race.
The outer race of the one-way clutch is splined to the overdrive ring gear, which is splined to the center shaft. The center shaft is centered by the forward planetary assembly and is laterally held by needle bearings on the center support and the overdrive planet assembly. The center shaft is splined into the forward clutch cylinder.
Two friction clutches are assembled in the overdrive planet assembly. The coast clutch is splined between the coast clutch cylinder and the overdrive ring gear. The coast clutch is activated to perform engine braking in MANUAL 1, MANUAL 2 and third gear with the transmission control switch engaged.
The overdrive clutch is splined between the case and the coast clutch cylinder. The overdrive clutch holds the coast clutch cylinder and, in turn, the overdrive sun gear, to permit the planet assembly to overdrive the ring gear.
--------------------------------------------------------------------------------------------
Forward Drive System
The forward drive system consists of the forward clutch cylinder, intermediate brake drum, intermediate one-way clutch, input shell, forward ring gear, forward ring gear hub, forward/reverse sun gear and the forward planetary carrier and forward planetary gears.
The forward clutch cylinder is splined on the center shaft. The forward ring gear is piloted on the forward ring gear hub. Thrust bearings on the forward planet assembly and forward clutch cylinder hold the forward ring gear hub in place.
The intermediate brake drum is radially supported by bushings on the center support and is laterally controlled by thrust washers on the forward clutch cylinder and center support. The intermediate brake drum has the inner race of the intermediate one-way clutch press-fitted on its pilot. The intermediate one-way clutch's outer race is splined to the intermediate friction clutch, which is splined to the case. The intermediate brake drum has lugs that are slotted into the input shell to form a mechanical connection. The input shell is splined into the forward/reverse sun gear. The forward/reverse sun gear is common to two planetary gearsets. The forward planet is splined to the output shaft and is laterally positioned by needle bearings on the sun gear and on the forward clutch cylinder, as shown in the following illustration.
Two friction clutch assemblies, the direct clutch and the forward clutch, are shown with the forward planetary assembly. The direct clutch assembly splines the forward clutch cylinder to the intermediate brake drum. The forward clutch assembly splines the forward clutch cylinder to the forward ring gear. The forward clutch is activated during all forward gears. While in third or fourth gear, both the direct and forward clutches are applied to hold the forward planetary assembly and enable it to act as a solid shaft.
In second gear, the intermediate clutch assembly holds the forward/reverse sun gears. It is applied, along with the intermediate one-way clutch, to hold the intermediate brake drum, input shell and forward/reverse sun gear. In higher gears, the one-way clutch overruns.
----------------------------------
Low and Reverse Drive System
The reverse planetary assembly consists of the reverse planetary carrier, reverse planet gears, the reverse ring gear, the reverse ring gear hub, the reverse clutch hub and the low-reverse one-way clutch assembly.
The reverse ring gear hub is splined to the output shaft and to the reverse ring gear. The reverse ring gear hub is laterally held by a needle bearing on the inner race of the low-reverse one-way clutch and a snap ring on the output shaft. The reverse planet assembly is splined to the low-reverse clutch hub. The low-reverse clutch hub is connected by the reverse clutch to the case. The inner race of the one-way clutch is bolted to the case.
The reverse clutch assembly is activated in REVERSE gear and in MANUAL 1. The reverse clutch bypasses the reverse one-way clutch during coast and MANUAL 1. The reverse clutch holds the reverse planet assembly in REVERSE gear to enable the sun gear to drive the reverse ring gear in the opposite direction.
-------------
Apply Components
The following information describes the operation of the three 4R100 one-way clutches.
One-Way Clutch—Overdrive
The overdrive one-way clutch, shown in the following illustration, transmits engine torque from the overdrive sun gear to the overdrive ring gear in first, second and third gear range. The overdrive one-way clutch transmits power when the sprags are engaged between the inner and outer races. The inner race is splined to the coast clutch cylinder, which in turn is splined to the overdrive sun gear. The outer race is splined to the overdrive ring gear.
The overdrive one-way clutch engages whenever the overdrive planetary system attempts to drive the overdrive sun gear clockwise when the overdrive ring gear has a counterclockwise torque from the vehicle. When torqued counterclockwise, the overdrive one-way clutch engages and acts as a wedge to lock the sun gear and the ring gear together. During coast, the overdrive one-way clutch enables the ring gear to overrun or spin at a faster rate than the sun gear.
The overdrive one-way clutch overruns when in overdrive (fourth gear). In overdrive, the coast clutch cylinder is held by the overdrive one-way clutch, which in turn holds the overdrive sun gear. This causes the overdrive planet assembly to walk around the sun gear and overdrive the overdrive ring gear. The inner race of the overdrive one-way clutch is thus held stationary while the outer race is allowed to overrun clockwise.
--------------------------------------------

left and push the shifter into the floor like stabbing down ten it will go left a little more and push forward and you will be on your way in good ol R