You may try to see if you could use an externally enclosed hard drive location
as a new installation, for a new OS X download from Internet Recovery, so the
internal hard drive may not be overwritten... There are links from Recovery
pages in Apple support. (But this may not be possible with a failed Mac.)
How to install OS X on an external drive connected to your Mac - Apple Support
Or create a bootable installer of the OS X in your computer, on an external USB
flash drive or other, using this: http://diskmakerx.com/
However in the attempt to boot into OS X Recovery, what happened? Did you
hold the keys down for awhile after the restart tone, then let go, or try holding
them down longer to see if that little difference mattered? And did you try more
than three times, to get into the computer using Recovery?
If you can get past the desktop and access OS X Utilities, there are options.
One of them would be to attempt to reinstall the OS X. Another would be to
see if Disk Utility can repair the system, and a few others.
• General ideas, here: (incl. second means to attempt access to Recovery*)
http://pondini.org/OSX/RecoveryHD.html
"...* Start your Mac while holding down the Alt/Option key. That will bring up the Startup Manager, showing all possible startup volumes"
• Apple OS X and Time Machine Tips:
http://pondini.org/OSX/Home.html
Given you state the computer is relatively new, there would be good reason to
see if the Apple Store (retail official) in your area has Genius area staff and if
you can get an appointment or reservation to have this issue checked into and
have a diagnostic performed. There may be some kind of hardware issue, there.
If so, then some kind of repair or other action may be done to resolve the problem.
http://www.apple.com/retail/geniusbar/
{If there is no Official Apple retail Store, only Authorized Apple resellers &/or
authorized service providers, you may still be able to get help; some locations
may charge usual and customary fees for shop time or diagnostics; independent
authorized Apple affiliates may operate under different rules than official Stores.}
Not knowing if you have any previous experience with OS X (older or newer)
I'm not quite sure what to suggest; some things I know about may require a
few steps in advance of a problem, such as backups or external drives with
system clone that can test/boot the subject computer to check internal drive.
Since your post appears to have been here for some time, and we're looking at
a weekend interval and difference in the time of day in these time zones, hard
to say who may be online (sooner or later) across the world; and of them, who
may have ideas that they can translate into a course of workable action for you.
I'd try OS X Recovery again, and note the info from the pondini linked page...
He's not around anymore and we're lucky that someone has kept the URL up.
At near 3AM local time, I'm going offline...
Good luck in this matter! 😎
