Should I just bury my iMac?

I don't see a problem. You are booted into Recovery Mode. Here is an Apple article with various startup screens you may encounter:

If your Mac doesn't start up all the way - Apple Support

For an iMac from the 2011/2012 era, most likely the internal Hard Drive has failed (or is failing). Unfortunately you neglected to provide any details on what led you to Recovery Mode here. If the internal Hard Drive is bad, then none of the information in the Apple article I linked will help you (or at least not for long).

You can try installing macOS onto an external USB3 SSD to see how that works out.

Use Disk Utility to erase an Intel-based Mac - Apple Support

Depending on the exact model, you may encounter difficulty reinstalling older versions of macOS because Apple's online installers are not being properly maintained, although there is usually a way to get around many of those issues if we are informed on which OS you are installing and the exact error encountered.

For a 2011 iMac which can boot into macOS 10.13 High Sierra's online installer using Command + Option + R, you may need to use Fix#3 in the following article:

https://mrmacintosh.com/how-to-fix-the-recovery-server-could-not-be-contacted-error-high-sierra-recovery-is-still-online-but-broken/

Hopefully if you have a 2012 iMac, then you should be able to boot into the macOS 10.15 Catalina online installer with Command + Option + R.....AFAIK, there has been no reported issues with its online installer.

Some Macs regardless of the keys used to enter Recovery Mode......some Macs may only boot into the online installer for the version of macOS which originally shipped with the computer from the factory. In that case, you may encounter some issues and may need to perform the erase of the external destination drive a bit differently. If this happens, we again just need to know the details to assist you.

FYI, you will need to make sure to erase the whole physical external SSD (will destroy all data on it) before you can select the "Reinstall macOS" option. With macOS 10.13+ installer, you will need to click "View" in Disk Utility and select "Show All Devices" before the physical drives appear on the left pane of Disk Utility. With macOS 10.11+ installer, you will need to erase the whole physical drive as GUID partition and MacOS Extended (Journaled).

If you are booted to a macOS 10.6 to 10.10 installer, then you will need to select the physical drive and Create a single partition with the MacOS Extended (Journaled) file system as noted in the following article (disregard the details for booting the installer....the critical part is using Disk Utility to properly prepare the external destination drive).

https://eshop.macsales.com/tech_center/formatting/Mac_Formatting_6-10_R3.pdf

FYI, when asking for assistance, you may want to review the following article which has tips for what information to provide:

Writing an effective Apple Support Communities Question - Apple Community

robloch wrote: Tried everything. Had my iMac since 2012. Should I just say farewell or take it in to the Apple Store repair? Thanks

You don’t indicate what the problem might be. Graphics? Hard disk? Something else not working?

Do Diagnostics show anything useful? Use Apple Diagnostics to test your Mac - Apple Support

A third-party repair provider will probably be willing to at least investigate the problem, but investments in a fourteen+ year old Mac are entirely your choice. I would usually look to unvest in a less old (working) iMac.

Donno if it's the photo, but the graphics do look wonky. If that is what you are reporting here — again, you don’t actually indicate what’s wrong — then I wouldn’t invest in a repair for this, as it’s probably going to involve the mainboard.

I would first have a Celebration of Life ceremony for its 14 years of existence, then recycle the Mac so it's spirit will live on.

I would not put any money into this machine where it could be better spent on a newer device.

Just my opinion.

Hi,

It seems to me, there is no problem on your iMac. Disk can't find out when you install macOS, say High Sierra I suppose or something?