寝ちゃわなきゃ is a very contracted form.
Starting from the fully expanded version, this developed roughly as:
I presume you understand the ～なければ + いい construction, so I won't explain that here.
In response to your comment. :)
～なければ is what you get from ない + conditional ～ば, and it means "if ～ isn't the case / if ...