I am assuming goats are pretty similar to sheep, so full tummies, warm ears and mouth, and a yawn and stretch when they stand will tell you they are ok. If they are full then they won't be interested in the teat until they are hungry again.
If the wee one isn't nursing and you can't get him to take from a bottle, tube him. If that isn't possible, you can inject glucose into the abdominal cavity, but only if you are sure how to do it - vet otherwise. He will get beyond the point where he can suck and digest food, so important to get glucose in him, then warm him up.