Why would you think it is not an shifter linkage adjustment or operation issue???? The fact that you can shift it into reverse with the lever on the side of the transmission tells me that it is EXACTLY a shifter adjustment/function issue. More than likely the drum latch to be specific.
Lets go through how the shifter works on the JD 4010.
1) When you move the lever left and right there is a latch (#6) that goes into slots on the quadrant drums (#11 and #17) to hold the one you are not using in position. You can see it work with the dash cowling off. It is just a flat piece of steel with a slot in it that rides on the bottom of the gear shift. (I think this latch not working is your problem. Read on down an I will try to go through it)
2) When you hold the lever to the left, out into the range quadrant (#11). You have Park, four speed ranges and a tow position. You are actually moving the drum/quadrant with the lever. The lever does not hook directly to any linkage.
The latch should be holding the speed quadrant still. These ranges are NOT synchronized. You should be stopped when shifting them. The "shock' looking thing (#32) is the PARK spring. So when you push the shifter forward the shifter can move into park with the gears not quite in line. The spring applies force to the shifters so when the tractor moves just a little it completes the shift into park. This shifter HAS ZERO to do with the reverse shifter. If you adjusted it you adjusted the WRONG one.
3) When you have a range picked out then you can move the lever to the right into the speed quadrant/drum (#17). Here you have low range forward. High range back and reverse further back. These shifts are synchronized. The latch should be rocked over into the range quadrant holding it in place.
So basically you have two shifters working off of one lever. It just depends on whether you have it to the right or left.
So Justin, this is a basic out line of the shifter operation. Now to help you find your problem.
1) Remove the cowling that goes over the top of the dash. You need to be able to see the shifter, latch and quadrant/drums.
2) Shift the tractor to the first range back out of park.(1st, 3rd and low reverse) Then move the shifter to the right into the speed drum. You should see the latch (#6) move into the slot on the range shifter.
I think right there is your issue. The latch is not locking the range shifter into position. Several things can cause this. The most common is that the cross pin (#23) is not holding the drums together. If the linkage is out of adjustment and the latch misses the slot you can force the drums part. That can push the snap ring (#24) off of the cross shaft. The the drums can then float too far apart. Also the bushings in the shifter pivot and drums get worn so that the drums can float apart and the latch misses the slots. I have seen the pin fall out of the latch too. So check it out.
So if the latch is not holding the range drum the range drum will move with the speed drum when you shift back into reverse. The transmission maybe in reverse but the range shifter is between ranges. So in effect it is in a kind of neutral. That is why you can hear the gears turning but nothing is moving. The speed gears are on the top shaft. The range gears are lower. So the top shaft is spinning but the lower gears are not connected like they should be. You also will usually get gear grinding just as often as you get the false neutral.
To start adjusting the linkage you need the make sure the drum latch is working. When you get it to work you will need to re-adjust the shifter linkage you moved.
With the shifter in park the right drum/quadrant should be held in place with the latch. Move the shifter back in the first range. This should line up with the slot to go into 1-3 and low reverse. Look at the latch and see if it is lined up with a slot in the range shifter. (The detent springs and plungers are on the side of the tractor. If you can't feel them then you have other problems, but they do not fail as often as the latch/shifter does) So you can "feel" when the range shifter is in the first range. So now you just need to make the shifter linkage/drums line up correctly. Adjust the range linkage(this is the on with the spring on it) so that the slot lines up perfectly centered. (Just lossen the jam nut at the top and turn the whole rod from the bottom. This is easier than taking the pin out of the top yoke and turning it)
Now move the shifter out into the speed drum/quadrant. Now watch and you will see the speed linkage move when you go to 1st, 3rd, or reverse. The range linkage should not move at all. Now look behind the right battery box at the shifter arms on the side of the transmission. With the shifter in 1st gear unhook the rod off of the shifter arm at the bottom or transmission end. You can shift the arm by hand with a little force. You may need a adjustable wrench to be able to shift it. You should be able to feel the detents real well right there. The shifter arm needs to be all the way down with the detent holding it in position. To do this, shift it down all the way and then wiggle it a little back up and you will feel when it is centered. Now adjust the shifter rod length to go into the hole in the shifter arm with out moving the arm at all. I usually like the shifter lever to beck back off the front of the drum/slot an 1/8 to 3/16 of an inch. You want it to shift the arm all of the way into low gear/range but it also has to shift correctly into 3rd(high range) and reverse. So too big a gap will effect the other two. Do not put the cotter pin in right now.
Now move the shifter back into 3rd gear. Go back down to the shifter arm on the transmission. Take the rod out of the arm. Wiggle the arm and see if it is in the detent. It should be centered just like 1st gear was. (As the shifter linkage wears everywhere you some times have to split the middle on adjustments. The rod may not exactly hit the hole on the arm. You have to make it work the best you can.) If it is centered than move the shifter lever back into reverse. The arm should detent and hold there just like 1st and 3rd. If it does then install your cotter in and everything is adjusted in the shifter now.
This is not hard to do. It is hard to explain in an email. So if your are confused with my description email me we can exchange phone numbers and I can walk you through it that way.
