Have you wormed her recently or treated her for coccidiosis? If so, what products did you use and how did you administer them and for how long?
You can get a dog/cat vet to do a fecal float to check for worm species so you can get a targeted medication for the species found. You can also pick up things like coccidiosis or giardia, etc. from a fecal float test. Normal vets, not just chicken vets, can do a fecal float - finding one willing is the trick, you may have to call around. Once a vet identifies the species, come back on here to get dosage instructions, and then compare to what your vet is saying. Not all vets know much about chickens, and you may at times get better advice from seasoned chicken keepers.
Alternatively, you can take a guess and treat them with what you think best and hope for the best. Deworming and treating for coccidiosis isn't going to hurt them as long as you have the correct product and dosage. It might not help them depending on what's actually wrong, but it can't hurt, IMO.
Green poop is generally a sign of a bird that is starving. But she's also not eating and not acting active, and hasn't laid an egg in 2 weeks. What have you tried to get her to eat? Has she lost weight? Is her keel bone visible?
It's about time of year when birds start to molt, so check to see if that's the case - this would explain the lack of eggs.
For the not eating, have you tried raw egg yolk? That's a tasty treat. Also chicken probiotics in yogurt or feed moistened with water or yogurt. Nutridrench dribbled into their beaks can sometimes stimulate their appetite - it's molasses water plus some vitamins, from what I can tell, and helps them be a bit more alert and willing to eat. Make sure not to put the dropper to far back into the beak, just get it on her tongue a few times, or hold her head sideways to the ground and dribble it across the beak opening so gravity pulls it inside. She'll suck it up with her tongue.
4 years is old for a production egger. They often pass from reproductive issues and cancer. Not knowing what the genetics are in your bird, since Americanas are a mix, she may have production egger in there and just be at the end of her natural life. Or she could have developed some type of reproductive issue or cancer - these are generally not treatable by backyard flock keepers.
If more birds in your flock become sick with the same symptoms, that's when most keepers consider sending a recently deceased bird off for an autopsy to figure out what's up. But with only one bird sick, it may not be worth the trouble unless you really want to know. There's special procedures, so search on here for details if that's a route you want to go before your bird passes.
Sorry you're dealing with this. Hope you find a way to help her and that she recovers. Crossing fingers for you!!!