I don't know much about crows, but after nursing two sick chickens this winter until their death it seemed the end for the crow was near. Pointing it's head into the air, something called "star gazing"... a creepy spiritual sort of movement they do when life is leaving their body. I still took it to my spring water to see if it had interest in drinking, and it did. That gave me a glimmer of hopeless hope.
I put the crow on some leaves in a box where it could be peaceful and safe, I started feeding it with a dropper- water and mushed up food, rice milk... anything it seemed to like.
It knew when i was going to feed it, and opened it's mouth like a baby in a nest.
Eventually it's one eye that wouldnt open, opened wide and it became very alert, less lethargic. But still the head turned around, pointing to the sky continued.....
My cat toots was curious about who was the latest patient in the blue box...