El Capitan installation failed, please help..

Cmd-r is not Safe Mode, it is Recovery, but it is where you needed to be.

Are you sure it actually booted into Recovery? Repair will be disabled if you start up from the same volume you are trying to repair. If you were in Recovery, you should have been able to Repair.

If you don't already, back up your Mac.

I would erase the drive in Recovery, then restore from your Backup. Then try the upgrade again. If the Installer is not saved on your Backup, then make sure you move it to an external drive so you don't have to download again.

You have a corrupted filesystem. Backup your files, repartition and reformat your drive, and reinstall your previous system:

Install or Reinstall OS X from Scratch

Be sure you have backed up your files because the following procedure will remove everything from the hard drive.

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.

Erase the hard drive:

1. Select Disk Utility from the main menu and click on the Continue button.

2. After DU loads select your startup volume (usually Macintosh HD) from the

left side list. Click on the Erase tab in the DU main window.

3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on

the Security button and set the Zero Data option to one-pass. Click on

the Erase button and wait until the process has completed.

4. Quit DU and return to the main menu.

Reinstall OS X: Select Reinstall OS X and click on the Continue button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible

because it is three times faster than wireless.

This should install the version of OS X that you had installed.

The startup drive is failing, or there is some other internal hardware fault.

Back up all data on the drive immediately if you don't already have a current backup. There are ways to back up a computer that isn't fully functional—ask if you need guidance.

Make a "Genius" appointment at an Apple Store, or go to another authorized service provider.

If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.

Keeping your confidential data secure during hardware repair

Apple also recommends that you deauthorize a device in the iTunes Store before having it serviced.

*An SSD doesn't need to be zeroed.

If you want to preserve the data on the startup drive, and it's not already backed up, you must try to back up now, before you do anything else. It may or may not be possible. If you don't care about the data, you can skip this step.

There are several ways to back up a Mac that is not fully functional. You need an external hard drive or other storage device to hold the data.

1. Start up from the Recovery partition, from Internet Recovery, or from a local Time Machine backup volume (option key at startup.) Launch Disk Utility and follow the instructions in this support article, under “Instructions for backing up to an external hard disk via Disk Utility.” The article refers to starting up from a DVD, but the procedure in Recovery mode is the same. You don't need a DVD if you're running OS X 10.7 or later.

If you use FileVault 2, then you must first unlock the startup volume. Select its icon ("Macintosh HD," unless you gave it a different name.) It will be nested below another disk icon, usually with the same name. Click the Unlock button in the toolbar. Enter your login password when prompted.

2. If Method 1 fails because of disk errors, then you may be able to salvage some of your files by copying them in the Finder. If you already have an external drive with OS X installed, start up from it. Otherwise, if you have Internet access, follow the instructions on this page to prepare the external drive and install OS X on it. You'll use the Recovery installer, rather than downloading it from the App Store.

3. If you have access to a working Mac, and both it and the non-working Mac have FireWire or Thunderbolt ports, start the non-working Mac in target disk mode. Use the working Mac to copy the data to another drive. This technique won't work with USB (except on a MacBook Retina with a USB-C port), Ethernet, Wi-Fi, or Bluetooth.

4. If the internal drive of the non-working Mac is user-replaceable, remove it and mount it in an external enclosure or drive dock. Use another Mac to copy the data.