Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your dog threw up several times Thursday night, then threw up a chewed ballerina slipper and hasn't wanted to eat or drink since then. I am very concerned that he remains lethargic since.
For most dogs that eat foreign material and vomit the object back up their symptoms resolve once the foreign material is out, because the irritant is gone.
The fact that he is still sick and not eating, and especially because he is lethargic, tells me either damage was done to his intestinal tract or there is more material still in his gastrointestinal tract that needs to be addressed.
I highly recommend he be seen today. This has already lingered too long.
If you absolutely cannot have him seen immediately to try and settle his stomach you can give either:
1) Pepcid-ac (famotidine) at one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at one 10mg tablet per 20 to 40 pounds of body weight every 24 hours.
These will reduce stomach acid and should help if this is related to simple nausea and gastrointestinal irritation from eating something he should not have.
Starting a couple hours after the acid reducers small amounts of water or ice cubes given frequently are fine as he needs fluids after all that he has lost with vomiting.
You can give pedialyte to replace electrolytes too but Gatorade is much too high in sugar which can make intestinal irritation worse.
If things are going well after the acid reducers start a bland diet of 1/3 boiled hamburger (or white skinless chicken), all fats and juices drained off mixed with 2/3 boiled, plain white rice. Feed several small meals a day. Once he feels better (no vomiting for 48 to 72 hours) start mixing in his regular dog food very slowly. Less bland more regular with each day. It should take a week or so to convert him back.
If he is continuing to vomit or refusing to eat and remains lethargic, it would be best that he see a veterinarian now.
If he has a tense painful abdomen, becomes even more lethargic, begins vomiting again or runs a fever greater than 103.5F then he really must be seen by a veterinarian as soon as possible.
Best of luck with your little one, please let me know should you have any further questions.