不，一点儿也不。

并不 is wrong 没关系 is right

What is the rest of the sentence? If someone says: "thank you" then and you reply no, not at all, then "没关系" or "不客气“ (You're welcome) is correct. However, if the sentence is to start "no, not at all..." then the following translations may be better: 不，绝对不是。。。 不，一点都不是。。。 不，并不。。。

才不是

Could I use 沒關係 answering someones' compliment?