This is a common fault on earlier hysters I've seen it many times.
It sounds like somebody has put the wrong oil in the transmission it does not run on atf.
The lining will have dried out and fallen off the clutch plates jamming up the clutch pack so it is always engaged, unfortunately the only fix is a transmission strip and new clutch plates in both packs. Not a hard job or mega expensive but time consuming
Anthony,
Since you can press the forward pedal switch and lift stops going in reverse, I would inspect all wiring and switches related to the travel pedal. Swap forward switch with reverse and see it changes the constant travel to forward. If so replace switch, if not make sure all wiring is good. Possible failed trans. Good Luck.