By 'open by hand' do you mean with the trolley released or by helping it by hand?
How does it travel open/close manually?
Without knowing what type of opener you have, see if this applies: Unplug the operator and remove the outside cover. Inspect the nylon gears inside the operator and see if there are any shreds of plastic or missing teeth on the gears.
What is the brand (not that matters much, there pretty much all chamberlins)?
Is it chain drive, belt drive, worm gear?
How old is the unit (could be just a bad motor which cost almost as much as a whole new unit)?