Day 2, settle down there pal. Any dog is going to be timid after moving to a new home, especially a puppy and especially a Shiba.
Dogs not eating is this circumstance is perfectly normal. You can try adding a little warm water to the food (brings out the taste and smell) if you are worried about him being hungry, but he isn't going to starve himself. He will eat way before then. If he doesn't eat breakfast on the 5th day then you should probably take him to the Vet. If he hasn't been drinking you should go to the vet asap.
The lethargy is also perfectly normal in this situation. Curiosity will slowly replace fear as he grows bored. He will begin to explore you, the house, and eventually other people.
I adopted a 4 year old female Shiba used as a puppy mill breeding dog (basically kenneled her whole life with little to no human interaction). The first 3 days with me she didn't eat. The first week she rarely left her kennel. After week 2 she was glued to me wherever I went in the house (but still didn't like to be approached). 3 weeks and she would let me pet her. 5 weeks and my parents could pet her. 2 months and she started coming to me for attention. 3 months she started playing with toys. I've now had her for 6 months and she still jumps at fast movements, lays down in her corner of the living room whenever we have company over, and refuses to be hugged/held (prefers arms length affection). She is extremely goofy and fun when in her comfort zone though. Walks were all she enjoyed when i first got her and even after 6 months of nail trimmings and a few baths she has yet to Shiba scream.
So basically what I'm saying is fuck your parents. That is your dog now. He is dependent on you whether he knows it yet or not. He will become attached to you, its in his nature. He may never be a friendly dog to strangers or impress with lots of tricks. But I promise you that at the heart of every Shiba is a quirky, fun, mischievous attitude.
A few tips:
Take him on lots of walks (and even a brisk jog if he does well on leash and keeps up). Get the blood and dopamine rolling in his system and he will open up a lot faster. The first dozen or so times my Shiba actually played was after exercise. You will know when he enters play mode when he starts dashing around and play bowing.
When he starts exploring let him do it at his own pace. Just continue what you are doing and watch him sniff around out of the corner of your eye.
Get him interested in... well, anything. Get a rawhide from the store, or shove food in an old stuffed animal (you can buy them cheap at thrift stores/goodwill). Let him tear the toy to bits to get to the treats.
You should try to get him to the Vet for a general check up if you haven't. Nothing he is doing seems out of the ordinary for the situation, but any new dog should get a check up. If money is an issue some vets will do the first visit free for rescued dogs.