black screen when in use on 2011 iMAC 27"

Welcome to the Apple Support Communities.

Yes. Your iMac is obsolete (Obtaining service for your Apple product after an expired warranty - Apple Support), meaning it cannot be fixed.

Your best bet is to purchase a new Mac, unfortunately.

Jack

Your HD has failed and should be replaced. That being said, as mentioned your iMac is almost 12 year old and is VERY obsolete and has no value. It cannot run current versions of Mac OS, it is slow, it cannot run current versions of many 3rd party apps and the list goes on. Please remember computers age and wear out just like a car, dishwasher, faucet or anything else.

Have you considered replacing it with a more up-to-date Mac? You have many many options open to you so this is something you may want to think about.

As an obsolete model OEM replacement parts are no longer available so it cannot be repaired by an Apple Store and might not be repairable by an authorized service provider either. However independent or DIY repair using generic, aftermarket, or salvaged used parts might still be possible depending on exactly what went wrong.

Could you better describe this 'black screen of death'? Does the computer still successfully starting up? Is the entire computer spontaneously shutting down? Something else? It is possible the HDD error code is a separate unrelated issue.

I have a soft spot for keeping old 2011's running, but to be honest you might do better buying a replacement rather than investing time/money in fixing the old unless this has high nostalgic value.

Replacing a computer every 12 years is not "constantly buying...". Lets say you paid $2500 12 years ago, that comes out to:

$2500 / 12 years = $208.33 per year

$208.33 /12 months = $17.36

In short you have gotten your monies worth out of the thing. It's time to replace it now!

No. It’s still obsolete.