Mac does not boot (startup drive is corrupted?)

Internet Recovery Mode is an Internet-based version of Recovery Mode found on newer Macs, which loads recovery tools from Apple’s servers. With Internet Recovery, you can reinstall OS X and troubleshoot issues in the unfortunate scenario of your Mac’s startup disk having become corrupted or completely unreadable.

How to enter Internet Recovery Mode
To enter this mode at any time, do the following:

1) In the Apple menu, choose Restart or power on your Mac.

2) As the computer restarts, hold down the Command (⌘) – Option (⌥) – R combination immediately upon hearing the startup chime.
Hold the keys until the animated globe appears on the screen. “Starting Internet Recovery,” the message reads. ”This may take a while.”
If you own a Mac notebook, make sure you’re using the built-in keyboard to enter Internet Recovery Mode as the keystroke may not register on external keyboards.

3) In the next step, a Wi-Fi menu appears. Internet Recovery needs an Internet connection to load the recovery tools from Apple’s servers. Click the menu to display the available Wi-Fi networks, and then select one to connect to.
If you’re connected to the Internet using Ethernet, you don’t have to connect to a Wi-Fi network during Internet Recovery.

4) If this isn’t an open Wi-Fi network, you’ll be asked to type in your password. Press Enter on the keyboard or click the checkmark symbol to continue.

5) After your Mac has connected to the Wi-Fi network, it’ll download a recovery system image from Apple’s servers and start from it, giving you access to the recovery tools.
Depending on your Internet connection, this may take anywhere from a couple of minutes to up to an hour, or longer. Connect your Mac to the power adapter so that it doesn’t run out of juice whilst it’s loading Internet Recovery from Apple’s servers.

6) If all goes well, you’ll be presented with the OS X Utilities window.
Choose the option you want to use in this window or via the Utilities menu.

The recovery tools let you reinstall the version of OS X which was factory-preloaded on your Mac, restore the computer from a Time Machine backup, check the connected disks for errors with Disk Utility or search for help online using Safari.