Apple Hardware Test issue

I believe the -2002D error is an issue with network connectivity.

Ensure that your wi-fi connection is behaving. Reboot your network router, reconnect the Mac to your network and try the diagnostic again. Better yet, connect your Mac to the router with an ethernet cable.

For troubleshooting the display issue, if rebooting your Mac doesn’t fix things, see if the problem still happens in Safe mode (hold the shift key down at startup). It can take much longer to safe boot (10 min) so be patient.

How to use safe mode on your Mac - Apple Support 

Safe mode disables loading third-party drivers, forces the OS to clear certain caches and logs and does other miscellaneous housekeeping. It's non-destructive to user data so is safe to do. Very often certain weird software behavior is corrected by simply logging in this way as a troubleshooting method. When you're in safe boot, the machine will not be at its best performance, especially with graphics, but that's expected.

Exit safe mode by restarting your Mac normally and re-evaluate the issue again.

If your iMac had macOS 10.12.6+ installed, then the system firmware was updated to use the online diagnostics. I believe that system firmware update broke the older offline diagnostic.

You can try rebooting your router and waiting at least five minutes for the router to finish booting before attempting to access the online diagnostics again.

What other issue are you having with the iMac?

See you duplicate posting for possible answer

https://discussions.apple.com/thread/253449339

I think D.I Johnson is correct, closest note I have is for 202u.

error "2002f" was reported when i had DHCP forwarder enabled on the router.

Error 2002u… Router needs DNS setting...

I was getting pretty frustrated at this point, but I finally found a post on the Apple Support forums by someone who was having a similar problem to mine (different error code, -2002U if I’m remembering correctly). With only one reply, I didn’t have my hopes up for a way out of this mess. Nevertheless, I looked it over.

The sole solution suggested going into my router settings, changing my DNS to 8.8.8.8 and/or 8.8.4.4 (Google’s public DNS server addresses,) and trying again.

https://medium.com/@lucchetto/2018-1-d4b628a2587e

Apple Hardware Test (AHT)

Description

Apple computers ship with a pre-installed suite of hardware diagnostic tools, known as Apple Hardware Test (AHT). In principle you can start them by holding the d key while booting. Newer models support holding option d to load AHT over the internet. Refer to the official Apple documentation for details: Using AHT on Intel-based Macs, Mountain Lion, Mavericks and Yosemite. Apple redesigned the AHT, now called Apple Diagnostics, for Macs introduced after June 2013. Consult the reference codes to interpret the results.

If however, you reinstalled an older computer from scratch, the diagnostic tools might no longer be available. Unless you have the original disks that came with your computer, there seems to be no way to restore the AHT.

It happens that Apple provides disk images with AHT for most computers, but does not make the links publicly available. Various blogs and forums, mostly Riven by Five and MacForum.ro have gathered a list of download links. The rest were obtained by scraping http://download.info.apple.com/Apple_Hardware_Test/ for all the links of the form 0(18|22)-\d{4}-A.dmg.

Even though there's no guarantee that this list is correct or complete, some links can come in very handy to whoever is trying to debug hardware problems.

You can use the following terminal commands to determine the model and board ID of your computer:

sysctl hw.model | awk '{ print $2 }'

ioreg -l | awk -F\" '/board-id/ { print $4 }'

Download the AHT for your computer model and use the contents to restore the /System/Library/CoreServices/.diagnostics folder, then reboot while holding d to start the diagnostic tools. Alternatively you may try with a bootable USB stick, as described below. This is also the preferred way on OS X 10.11 or later, where the System Integrity Protection (SIP) no longer allows writing to system folders.

When trying to open an old dmg you may get the error 'legacy image should be converted'. To convert it to a newer format, open Disk Utility, in the menu Images click on Convert and select the dmg to convert and save it under a new name.

Note that there is no one-to-one correspondence between hardware model and AHT. For some models no hardware test could be found, while others seem to have multiple AHT. As the differences are not clear, feel free to try them out, to see which one works best for your hardware.

https://github.com/upekkha/AppleHardwareTest