Changed the mod for ~/.. directory by mistake, made it 744, can't boot anymore
I would do two things to restore a Mac in this situation.


boot to recovery mode and run Disk Utility - repair the drive, the volume and then repair permissions.
Boot to recovery mode and run the installer. That should fix or log the exact directory that has improper ACL/permissions and re-create all basic mount points.


The installer log can be read in recovery mode boot if step 2 doesn't fix things and we can perhaps refine exactly what directory or directories are now messed up. There is a chance that you had a separate failure and your chmod was coincidental to the issue as opposed to causative.