Mac won't boot; get the Apple logo then it becomes a prohibitory symbol
This means that the Mac can't find a valid startup folder to boot from.

The solution to this is to reinstall OS X – power up your Mac while holding down Cmd-R, then select Reinstall OS X (or Utilities -> Reinstall OS X). 
Depending on what version of Mac OS X, you will want to select "Archive and Install" if you want to preserve your files. Follow the onscreen prompts to reinstall Mac OS X.

If you have a backup disk for your Mac, that's a bonus just in case the installation goes wrong.