Renamed /etc folder. I can't login anymore
I would try booting in single user mode (holding the Apple and S keys while rebooting), mount the hard drive (mount -uw /) and then check and rename etc as needed (there should be an alias at the root of the HD named etc pointing to /private/etc).

I would do an ls -al / and a ls -al /etc to see which directory name was changed and then fix the bad directory name with mv. Checking each directory would be important regardless of which fix you used (the one above or below).

If single user boot doesn't work, I would “Target Disk Mode” using another Mac (turn off the bad Mac, connect the two Macs with Firewire or Thunderbolt cable, start the bad Mac while holding down the T key), this will mount the bad Mac's drive as an external drive on the other Mac and you should be able to use the command line to change the name there.

Or, as someone else suggested, booting from the recovery partition.

Last resort is to reinstall the system, it should allow you to do that without wiping the drive.