MacBook Air won't start up, won't enter secure mode and repair in Disk Utility
It seems that you may be trying to fsck the wrong partition. You can use duskutil to find which disk is your boot disk

diskutil list


You're looking for something named usually "Macintosh HD" or "Yosemite". Try the fsck on that, and if you're still getting the "Resource busy" error, try to unmount it, either in the Disk Utility in recovery, or by using diskutil unmountDisk /dev/disk# and trying again.

Hope this helps!