So what you have on that machine is an old Sauer-Sundstrand 18 Series pump. The model number is 18-2081. For Sundstrand/Danfoss, anytime you see a "R" at the end of a model number, it indicates that it has been remanufactured.
The "LH" indicates that it is a Left Hand rotation pump (counter-clockwise). If the pump was sitting in front of you with its input shaft facing you, the shaft would need to rotate to the left, or counterclockwise.
Since we know that it is an 18 Series pump, we also now know that it is a closed circuit system. Oldnslo had already mentioned that based on the exploded view diagram.
Based on what you have described so far, my first thought would be to check for charge pressure. I believe oldnslo has also mentioned that in one of his posts. The problem with a direct displacement pump, is that you can force it into stroke without charge pressure. Without any charge flow, there is no oil in the circuit to send from the pump's rotating kit to the motor and thus no trencher chain movement.
The noise that you are hearing from the pump could be the charge pump running without any oil. If that has been going on for a while, then you may have an issue because those parts rely on an oil film to keep them from damage.
I would first start by making sure you have oil getting to the inlet of that pump. The inlet of that pump can be found on the diagram that is attached.
I would crack that hose fitting at the pump and see if oil is reaching the pump. If not, you will need to backtrack it to figure out where the obstruction lies. There may be a suction filter or screen that is plugged.
If you have oil at the inlet, then get a 500psi gauge and plumb it into the charge pressure gauge port and see what pressure, if any, the pump has when the engine is running. It should be at least ~100 psi. Some of the 18 series pumps ran fairly low relief settings so don't be surprised if it is at that level. It may be higher, but it shouldn't be lower than that.
In case you are not familiar with a closed circuit system, here is a system that should be similar to the one that is on your trencher.
Keep us posted on how your investigation goes. We can help direct you based on your findings.