Can you see the other end of the drain pipe?
Nope I imagine is goes down to an old french drain or some kind of basin
I would try and figure that out first (it might not be possible).
Because if the pipe were dump to daylight downhill somewhere, using a snake, water, pressure washer, or garden hose with spray nozzle to clear the dirt (and likely push it deeper into the system).
If it is a basin/dry well I might try using a combination of water and a shop vac hose to loosen and remove the material (to prevent more dirt form filling in the dry well).
It might be worth trying to map out your drain setup and its condition. My FIL has a 100+ year old house and all of the original drainage was clay tile. Not one of then was functioning when he bought the place (some were silted in and some had collapsed).