How to repair startup disk with El Capitan

Repair the Drive for El Capitan

1. Restart the computer and after the chime hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility and press the Continue button.
3. Then select the indented (usually, Macintosh HD) volume entry from the the side list.
4. Click on the First Aid tab in the toolbar and wait for the Done button to activate. Click on it, then quit Disk Utility.
5. Select Restart from the Apple menu.

If you have problems then please post a snapshot of what Disk Utility is showing on the screen. Your explanation is just too vague to be helpful.

To Post A Screen Shot

1. Press Command-Shift-4 which will change the cursor to crosshairs.
2. Hold down the mouse button and use the crosshairs to select the part of the screen you wish to capture.
3. Release the mouse button and the image will be saved to your Desktop.
4. Click on the Camera icon in the toolbar of the forum message editor.
5. Drag the image onto the Choose File button and click on the Insert button.

The above is only useful when running Disk Utility from the running system. If you boot from the Recovery HD, then you will need to snap an image using an iDevice in order to post the image here.

I started my Macbook in recovery mode and launched disk utility there, but then the disk's partition, which seems to need repairing is greyed out and I can't even run «first aid» on it.

If Disk Utility cannot mount the boot volume in OS X Recovery, then the drive has failed and requires replacement. For repair options use the Official Apple Support link above.