Sorry, I had to go tuck my own chicks in for the night.
Okay, if this isn't a digestive issue then we don't have a great chance anyway, so let's treat it like one and see if we can make a difference.
First, let's give the chick a little sweetened water to make sure we are hydrated and give a little energy boost. Mix lukewarm water with some honey, corn syrup, molasses, or other sugar source. Give it to the chick a drop at a time by touching the drop to the crevice of the beak where the top beak and lower beak meet...it should wick into the mouth on it's own. Wait for the chick to swallow and repeat. Try for at least 5 drops, preferably 10. Wait a bit and see if the chick perks up a little.
If the area around the vent looks swollen and pink, we're probably constipated. Soak the bottom half of the chick in warm water to help hydrate via the vent and stimulate pooping. Pat dry and put under a heat source. Repeat if necessary until can pass droppings normally.
If that doesn't work or doesn't seem to be the problem, give the chick a few drops of olive oil the same way you did the sugared water as the issue may be further up the pipes. This will lube things up. If the chick has perked up and is showing interest in eating, give it chick-sized grit. That way if it has eaten any shavings etc. the gizzard can grind them up so they can pass into the intestines.
You may or may not be able to pull this chick out of this condition. They are pretty fragile at this age. What I recommend is that you do a search for a list of items that are recommended to keep in your chick/chicken home emergency kit. Particularly since your farm store is 40 minutes away you probably should keep them on hand.