て form to joining sentences but in negative sense

Question

I'm learning about the uses of て-form, one of them is to joining sentences like

家に帰ってTVを見る
I come home and I watch TV

but if I want to apply a negative sense to the て-form, do I have to use the ないで or the なくて? Does either one work?

家に帰らないでTVを見なかった
I didn't come home and I didn't watch TV

家に帰らなくてTVを見なかった
I didn't come home and I didn't watch TV

Answer 1

If you just want to list two things you did not do in parallel, you can use し:

家に帰らなかったし、TVも見なかった。
I didn't return home, and I didn't watch TV, either.

The te-form doesn't work well for this purpose because it implies some relationship between the two actions.

家に帰らないでTVを見なかった is a rather unnatural sentence, but it would mean "I didn't watch TV without returning home." (or more literally, "Not-returning-home-and-watch-TV, I didn't do it.") Effectively, this is a rather convoluted way of saying "I watched TV only after returning home".

家に帰らなくてTVを見なかった usually means "I didn't watch TV since I didn't return home." This is an example of te-form for reason. It's better to say 家に帰らなかったのでTVを見なかった, though.

家に帰ってTVを見なかった almost certainly means "I didn't return home and watch TV". A sentence like this treats the two actions as one set. You need only one negation (ない/not), both in Japanese and in English.

Some (more natural) examples:

箸を使わないで食べなかった。
箸を使わずには食べなかった。
I didn't eat it without using chopsticks. (= I never failed to use chopsticks when I ate it.)

バスが来なくて学校に行けなかった。
I couldn't go to school because the bus didn't come.

See:

• ないで vs なくて: combining phrases with negative verbs
• して行｛い｝かない versus しないで行｛い｝く