Your OP said nothing about slow hydraulics, just that "bucket goes up and down but machine will not drive" - hence my first thought of safety systems.
I would say, and others may correct me on this, that if the coupler between the engine and the pump fails you would have no hydraulics at all. You say you have working hydraulics albeit they are slower than normal. Can you see any signs of frothing or bubbles in the hydraulic tank sight glass..? If not I suggest your next step is to inspect the hydraulic filter internally - you will need to cut it open to do this but can you find any traces of metal (either steel or bronze) in it..?