My experience/knowlege is limited to the 722.1xx/722.2xx automatic transmission. It may apply to newer transmissions, but I do not have the manual or experience with them, so don't treat the following as gospel
.
If the linkage checks out O.K., and it is an automatic, it sounds to me like the B3 brake band is not engaging. This could be because it is too loose (it is adjustable from outside of transmission), or the B3 servo might have a major internal leak (possibly repairable in-vehicle), or the band is completely worn out (need to remove transmission to replace).
If you remove the tranny oil pan, and valve body, you can use compressed air to verify correct operation of B3 servo/band. The B3 servo/band is used only for reverse.
You may find the piston/cylinder is damaged, however, beyond in vehicle repair
. The fact that it would get stuck in reverse doesn't sound like a simple leaky piston or wear to me
. See my experience with B2 cylinder wall wear in link:
http://www.peachparts.com/shopforum/showthread.php?t=131124
Also has nice pictures of tranny with valve body removed...