I actually saved a week baby once by making the baby open its mouth only hours after hatching (prior to its first shed) and administering baby food via a syringe (without needle, of course). I did this a couple times per day for the first two days. After that, the gecko slowly started acting normally.
I think it was the sugar that helped the gecko survive, so I'd venture to say that even sugar water or a non-citrus fruit juice (like grape juice or apple juice) would be even easier and more effective.
I would also advise you to keep the baby in the mid 70 degree range. If you keep it too much warmer, that will only speed up its metabolism, which will make the baby expend much more energy (calories) than necessary.
I should mention that the gecko I saved is still tiny (five months old and only about 5 grams) and has an underbite. I'm keeping it around as a pet, but because of that, I've decided that I'll let nature take it's course if I happen to get any week hatchlings in the future.
-Anthony
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Anthony Caponetto
www.ACreptiles.com