Running diagnostics I get -1007D. What does this mean?

Please follow the seps imhttps://support.apple.com/en-us/HT204156. I suspect a hardware failure which means you need to take the computer to your local Apple Authorized Service Provider to be diagnosed. Assuming you back up your data should be safe.

Are you attempting to use Internet Recovery with your Mac? Low negative number error codes typically indicate an issue with the Wi-Fi network that your Mac is connected to in order to enter this mode. Have you tried using this mode with your iMac connected by Ethernet?

tbeers1 wrote:

My iMac will not boot up. It shows the Apple logo and takes 12-15 minutes for the progress bar to finish. Then it just hangs - does not go to desktop.

The point where the progress bar appears is when your Mac is attempting to load kernel extensions.

Ref: If your Mac starts up to an Apple logo or progress bar - Apple Support

I concur with rkaufmann87 that, most likely, your Mac is having some type of hardware failure. If I had to guess, at this point in time, I would suspect the system drive.