That is interesting. I have been into a couple of these, but it has been a while, and my memory is rather quick. With that said, here goes:
If i recall correctly the ball and spring are mounted vertically up in the cover, i.e. the ball would shoot out right at the camera lens if you slid the shifter rail out of its guide.
Take the bolt out and move the rail and you can tell if the spring and ball are in place and operational. If so, I would wonder why it was done and carefully examine the synchronizer assembly on the mainshaft. 3rd and 4th on this transmission is synchronized and if someone before you trashed the synchronizer, whoever owned it may have just decided to lock out those two gears instead of fixing it. You really have nothing to lose by trying to engage 3rd and 4th, as easy as it is to pop the cover off.
In reference to your second question about slippage, yes, this machine is designed to slip. It is equipped with a torque converter just like in an automobile with an automatic transmission. If your machine easily spins its rear wheels in first gear, and also in second with poor traction or while prying with the loader, hence taking weight off the rear wheels, I wouldn't suspect a problem with that part of the machine.
The Case 580C through 580E are some of my favorite machines to work on, they are well-built and rather simple. Let us know what you find. I am keenly interested.
Dustin