ないで vs なくて How to correlate two or more phrases with negative verbs

Question

Can you use -なくて instead of -ないで in the following sentence, keeping the same meaning? What's the difference between ないで and なくて ?

病気になると、一切化学薬品や抗生物質を使わないで、鍼や指圧や漢方薬で直します。風邪の時は何もしないで暖かくして、寝ているだけです。

Answer 1

Peter Sells (1995) calls ないで as verbal gerund and なくて as adjectival gerund. When you have participial constructions, they do not make difference, but Sells notices that only the verbal gerund can be selected by an auxiliary verb:

食べないでおいた
* 食べなくておいた (Sells 1995:287)

Similarly to that, when you want to use these forms adverbially as in your examples, you have to use ないで. You cannot replace it with なくて. If you do so, they would be interpreted as participial constructions.

何もしないで暖かくする (ambiguous)
'not do any activity, and keep the body warm'
'keep the body warm by not doing any activity'

何もしなくて暖かくする (unambiguous)
'not do any activity, and keep the body warm'
* 'keep the body warm by not doing any activity'

Other than that, I do not know of a difference.

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Sells, Peter (1995) "Korean and Japanese Morphology from a Lexical Perspective" Linguistic Inquiry 26.2 MIT Press