OK, then first thing you need to do is get him to drink. Some people use red jello in the water to help that. He might just not have the energy. I'm assuming you haven't seen him eat either? His abdomen doesn't feel really full, like he's holding poop?
First, I'd check his vent. Use a warm wash cloth and place it gently against the vent - see if it's normal, see if it's clogged, etc. especially since there's a chance of dehydration. Well he IS dehydrated if he's not drinking.
Then, you'll want to give him a booster drink to increase his fuel so that he can drink. For most babies that age, I use a boiled egg yolk (freeze what you don't use for later use), a dab of plain yogurt (for the living bacteria therein), some water, pedialyte or a tiny bit of karo or honey or the jello, and some of their crumbles. Make that into a barely moist mash. I mix just a tiny batch - like a dixie-cup full - of this mixture.
Use some of that mixture and mix with more water, about a half dixie cup, til it's a little thicker than water. Then you can dip his beak into that or use a dropper on the *outside* of his beak on the side and see if he'll swallow it on his own. Do that as often as he needs to get him fueled back up. Then offer the drier mash to see if you can get him to eat.
Healthy baby poults are usually quite inquisative and curious creatures to a fault. If you poke your finger in something, they're usually right on it. He's weak, and needs fuel. Then hopefully you can use that curiosity to get him to eat.
Let's start there.
Oh yeah I have to give you the blackhead speech.
it was given to me, thankfully, and so I pass it on.
Baby turkeys ideally should be on a feed that contains histostat, a blackhead prevention medicine. I've done it without - but when they get older, there's no treatment medication for blackhead available and so you're stuck if they get it. Chickens carry, but are rarely effected by, blackhead. For this reason you're not really supposed to have them together. If you do, just know there's that risk.
I've always had turkeys without histostat with my chickens, but this year I'm wondering if that's wise. So learn from my mistakes and just know the risks.
Tada - speech over.
What kind of baby is he? We're raising two baby BBwhite poults at the moment, two just-adults, and have one two year old hen. Previously I raised bronzes.
And by the way, if he's a white turkey (likely BB white) you'll not want him to grow fast. That's why I actually didn't use turkey grower on my babies - because they are meant for slaughter and to grow very fast and be slaughtered before their legs give out. So you'll want a lot of space for exercise for the baby, not too much 'growing' food, slow growth if you intend him to be a pet.