[RadioKid]

"こんなに急ぎでなきゃ　家の 手入れも　しといたんだけんど。"

=> If the moving was not so suddenly, I could have taken care of the house.

>What I have learnt is that "nakereba" (-eba conditonal) means "if something not [happening]". Why DE nakereba? What is the purpose of the DE?

In this case, "DE" is "連用形" of "助動詞：だ" used for expressing "in a hurry" or "moving suddenly". (Sorry, I don't know the English word for Japanese Grammar words)