You may be able to contact the sales support in online Apple Store, and they should have
a record of the purchase of the Mountain Lion 10.8 download code. And also of the email
sent to you, somewhere in their internal records. This latter point, should apply to your
email account; unless you deleted the download code email from Apple.
If you can contact Apple support or even sales support, they may be able to re-send the
code again; providing they can find the record of that transaction. You should use the
method to create an offline installer from the download, such as suggested in earlier post
so it would be available, in case the hard drive fails or you end up needing to install the
OS X to an external hard disk drive, or other media such as USB flash (16GB or larger.)
• OS X - Contact Support - Apple Support:
http://www.apple.com/support/osx/contact/

Read the above article, specifically the section for 'Mountain Lion and Earlier'; and the
section Apps bundled with a Mac purchase. If you upgraded to Mt Lion 10.8.5 and
then got update or upgrade application versions to complete this upgrade to 10.8.5,
the App Store should have a record of those transactions. But maybe not.
{A change to the App Store does not show my as-shipped present computer list of paid
applications that accompanied the computer (bought within the last year) nor is the
list of unsupported updates (for newer than Mavericks 10.9.5 in my Mac) for use with
a later newer OS X. Since I did not get Yosemite, due to some questions I asked and
never got a timely answer about upgrade with new system installed (on the second
internal hard drive, my mac has two factory HDDs) without compromising Mavericks.
And now there has been issues by users of the same mac I bought, with El Capitan.
So I'm not wanting to find my hardware graphic processor fail due to firmware issue!}
The OS X Recovery has certain limits; the articles suggest them, regarding the use of
internet recovery for one kind of recovery; and the in-computer recovery for another.
For a computer that had its hard disk drive replaced with a new one, the original OS X
Recovery would not be in the computer. This is where an Apple Store genius could help.
Or an Apple Specialist, or an AASP; a retail authorized Apple service provider...
If you bought the extended AppleCare Plan, there would be no charge for help after
the complementary 90-days support. A genius in retail Apple Store is of no cost.
The Apple Support for your purchased OS X 10.8 should continue for 90-days after the
date of purchase; they should still be able to help after that duration has passed. Also
an Apple Genius in a retail Apple Store could be able to help restore that OS X. The
help could come from the link posted above, to contact them; or the main Applecare
phone number. The main online retail store has contact numbers in Contact Us page.
{To save a copy of the installer once it is downloaded and before it is run, is
an idea that can save a lot of time; instead of waiting again for a slow internet...}
• How to reinstall OS X on your Mac - Apple Support
That is discussed in this other article that covers similar ground:
http://www.macworld.com/article/2690806/how-to-install-mac-os-x-yosemite.html
Another way to make a copy of the installer for later re-use, is covered here:
http://diskmakerx.com/
Hopefully the Support people can assist in getting 10.8 Mountain Lion; either online or
in an official Apple retail Store with Genius bar. If you live in a country which has them.
Good luck in any event! 🙂