can you give a full model number? and possibly serial number?

but with that said, most transmisions in lift trucks work alot like they do in a car/truck. The torque converter does play a part but in most cases you'll find one of two things that will cause a transmission not to pull, one is low pressure due to clogged valves or filter/sump screen or possibly an inching valve problem.
second would be the worse case scenario of worn out clutch discs.
since you say you can feel it engage it could be either.
if i had a full model number i could see which model trans it has in it and can give you info on how to check it out.