Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your pup is somewhat lethargic, has refused to eat for 3 days and vomited something green.
Dogs that do not feel well often are mopey, so along with his vomiting and not eating I think he's just trying to tell you that he doesn't feel well.
Was the green material clearly a piece of a plant or just greenish liquid? Dogs that feel nauseous will eat plant material, and that could explain the green plant material. If this is the case he likely ate the plant in response to whatever is making him nauseous and not want to eat, and the plant is unlikely to be the real issue. If his vomit was more green fluid then dogs that have a gastrointestinal blockage or very abnormal intestinal motility often vomit green material as that is digested bile, bile that sits in the stomach for a while. Bile only refluxes back into the stomach when gastrointestinal motility is abnormal, such as with a blockage or poor gastrointestinal motility due to primary intestinal or metabolic disease.
Vomiting can be related to chronic pancreatitis, a dietary allergy or sensitivity, toxin exposure, a viral or bacterial infection, inflammatory bowel disease, internal organ failure, a full or partial gastrointestinal obstruction or even infiltrative cancers such as lymphoma. Because this happened soon after the dog park visit perhaps he ate something there that you don't know about.
Is he a fellow that eats things like rubber bands, toys other things he should not?
Because he isn't eating for this length of time I am very concerned about him.
Ideally he would see a veterinarian since this has been going on for more than 48 hours. Simple stomach upset should pass within 24 to 48 hours. They could examine him, run blood tests and possibly check radiographs and/or an ultrasound to evaluate him and know best how to treat him.
In the meantime they can administer injectable anti-nausea drugs and fluids to rehydrate him and rebalance his electrolytes.
If you cannot have him seen for whatever reason there are some things you can try at home, though if he doesn't respond quickly he should see a veterinarian.
At home to try and settle his stomach you can give either:
1) Pepcid ac (famotidine) at a dose of ¼ of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of ¼ of a 20mg tablet per 10 to 20 pounds of body weight every 24 hours
These are acid reducers and should help her feel better. They are quite safe and can be used for several days if necessary.
A couple of hours after giving the acid reducer I recommend offering soft foods mixed with water to make eating and swallowing more comfortable.
If he is refusing to eat even soft foods you can try offering meat baby foods or a bland diet of 1/3 boiled minced white skinless chicken and 2/3 boiled white rice mixed with some low salt chicken broth to make it easy to lap up and swallow.
If he continues to not eat and continues to vomit green material he should see his veterinarian or an emergency veterinarian for an examination, diagnostics and intravenous fluids and supportive care.
Please let me know if you have any further questions.