I know how stressed and worried you must be over this. From your previous post it sounds like you really did your background homework and are prepared to give this little guy the care he needs. Good for you.
A few things: You say it gets cooler at night? How cool? While nighttime temps should drop, I find that keeping some belly heat available at about 85 degrees F, 24 hrs a day, is a good thing. Babies also need a "cave" where they can hide. I personally put one on each end of the cage. Like was already suggested, try not to handle him to feed him right now if you don't have to. Just think how big and predator-like you must seem to a 4 1/2" baby. Dragons seem to subscribe to the "if I can't see it it will go away, right?" school of stress behaviors, hence the eye-closing. He may also have been tiring, from stress and just sleepy-time.
Do you have your lights on a timer? Regular light cycles are important. About an hour after he wakes up in the morning, and has a chance to get warm, try dropping the babyfoods thinned with water or Pedialyte on his nose like suggested, without removing him from his cage. It may take some time before he begins to lap, so fill the feeding syringe so you have plenty, but don't expect him to drink it all. Repeat throughout the day. Also offer a dish of very finely chopped greens/veggies/moistened pellets (if you're using them). Live prey may be too intimidating until he is acclimated.
It can take time to acclimate to a new environment and begin feeding normally, but you don't want to risk dehydration so keep up the food supplementation until he starts to eat regularly. You will also want to scoop up the first little poop you see, ASAP, baggie it and get it to your vet for testing, also ASAP. If he is diagnosed with parasites and prescribed medicines, come back here and ask about other things you should be doing alongside the medical treatment--these other things can make a world of difference to your dragon's overall well-being.
If he does not lap liquids at all get him to a herp vet for supportive care ASAP. If you don't know one and you are in an area with a local herpetological society, call for a recommendation or ask around her for anyone local to you.
Have patience, keep working with him and keep us posted. Best of luck to you and the little guy.
michele
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