Keep in mind, permission problems can be the file itself, such as /private/etc/sudoers, or anything above the file, such as the /, /private, or /private/etc directories themselves.
I just solved this exact problem for a user at macrumors, and it was ultimately the group permissions on / itelf!
Here's what the perms should look like
$ ls -lad / /private /private/etc
drwxrwxr-t@ 32 root admin 1156 Feb 18 15:07 /
drwxr-xr-x@ 6 root wheel 204 Nov 29 22:15 /private
drwxr-xr-x 87 root wheel 2958 Feb 19 19:27 /private/etc
in his case, the root directory was:
drwx---rwx+ 33 root admin 1190 Feb 14 23:38 /
Since sudo access isn't available, it's not surprising that commands that need to run as root (such as diskutil repairpermissions) would not work properly. To fix this, you must get root authority and fix the appropriate permission. Without access to sudo, single user mode is the most straightforward way to do this:
Reboot into single user mode (hold Option S while booting until it switches to text mode)
At the single user prompt, type: /sbin/fsck -fy
This checks the filesystem integrity
Then type: /sbin/mount -wu /
This mounts the root filesystem as read/writable.
Next correct the broken directory permission. For the example above, it was the perms for /, therefore:
Next type: /bin/chmod 1775 /
Type: /bin/sync
This will make sure the change is written to the filesystem.
Type: exit
Your mac will continue booting as normal and life should be good! sudo should now work. At this point, I'd recommend a repair permissions in Disk Utility to correct anything else that may not be right.