I am sorry to hear that your fellow was vomiting and drooling and now has refused to eat much of anything the past 4 days, and seems lethargic.
It's hard to know whether his lethargy is weakness from not eating and from dehydration and electrolyte imbalances that occur with vomiting or if that is part of the disease process that is making him not want to eat.
I understand that it is frustrating to run tests and have everything come back within normal limits, especially when your pup obviously feels poorly. But it is very important to know what isn't wrong to know to look next.
In most cases vomiting is triggered by eating something they should not, too much table food, too many treats or something they find outdoors.
More serious causes of vomiting include toxin ingestions, viral or bacterial infections, a dietary allergy or sensitivity, inflammatory bowel disease, internal organ failure (kidney or liver disease), pancreatitis, or a full or partial gastrointestinal obstruction. If he is a middle aged to older pup then an abdominal mass is also a possible cause.
In a young dog, especially if he never finished his vaccine series, a viral infection such as Parvo virus, toxin ingestion, or a foreign body leading to a partial or full gastrointestinal obstruction would be the most likely causes.
There are some things we can try at home, but if he's not improving quickly he should see a veterinarian for another examination, some further diagnostic testing, intravenous fluids and injectable medication to settle his stomach.
To try and settle his stomach at home you can give either:
1) Pepcid ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of one half of a 20mg tablet per 20 to 40 pounds of body weight every 24 hours
These are acid reducers and may help settle his stomach and get him feeling better and hopefully get his appetite back. Either one can be given for several days if need be as they are very safe medications.
In a couple hours when you give him water make sure it is in small amounts only. If he drinks too much too quickly that can lead to vomiting. You can also offer ice cubes to lick. To get some electrolytes in you can offer him a 50:50 mix of pedialyte and water.
If there is no vomiting for 2-3 hours after drinking offer a bland diet of 1/3 boiled, minced, white skinless chicken or boiled, lean hamburger and 2/3 boiled, white rice mixed with some low salt chicken or beef broth to make it easy to lap up and swallow. If he refuses that you can offer a little meat baby food. If he refuses both then he needs hands veterinary care.
But if things go well and he does eat and doesn't vomit feed him the bland diet for 2 to 3 days then slowly start to mix back in his regular food, a little more at each meal. It should take about 5 to 7 days to slowly convert him back to his regular diet.
If he continues to not eat or vomit even with the acid reducers, runs a fever (more than 103F rectally), or has a lower then normal temperature (less then 99F), has a tense painful belly he should see his veterinarian for another examination, diagnostics, injectable anti-nausea drugs intravenous fluids and supportive care.
Please let me know if you have any further questions.