hi Lewis ,serial number please, assuming you have checked the basics I would isolate the transmission hydraulic system from transmission electrical system.
you can operate the transmission manually.
disconnect the lockup ,downshift and upshift solenoid electrical connectors.
remove the plug on the transmission case ,on the opposite side of the shift card.
apply park brake and service brakes (front brakes as well)
place a 1/4 inch socket extension bar into the hole that plug was removed from and into the end of the selector shaft, rotate the shift lever in the clockwise direction to place transmission in neutral
start the machine and manually rotate the shift lever through all the gears
check that engagement takes place
CAUTION MACHINE CAN MOVE DURING THIS TEST
As a quick check of hydraulic operation refit all electrical connections . rotate shift lever anticlockwise and start engine. the shift lever should rotate back to neutral position
Further testing requires the use of gauges
if this is ok we can move on to the electrical system
A couple of things to check first
it has been known for the locating pins in the shift shaft and rotary actuator
to break and come loose .remove the shift card and the flexible shaft place a screwdriver into the slot that the flexible shaft came out of and try and turn with moderate pressure there should be no movement
like wise on the detent end (where the 1/4 inch drive is) there should be no loose movement
Mark