I think you may just be missing the internet boot.
When you try the Windows keyboard, are you using alt-D?
The timing that almost always works is to do a PRAM reset...
Restart while holding Option-Command-P and R.
You should hear the boot chime. Continue holding the same 4 keys until you hear the boot chime 2 more times.
When you hear that third chime, release all keys, and immediately hold Option-D
You SHOULD see the rotating globe, showing that your Mac is booting to Apple's servers, where the diagnostics will run.
Do you ever see the rotating globe - as on
this page? That can take several minutes to completely boot.
If you are still getting the internet boot icon, but it always stops at the "apple.com/support" with an error code - is it always that same code -6003D?
I cannot find any list of those codes, or any real help with deciding what to do to troubleshoot those errors.
I DO see that when it has one of those boot errors - it is usually a networking error of some kind.
Be sure that you have disconnected any external drives, including all USB devices or hubs. (ONLY power, keyboard/mouse, and network connection.
Do you have another network (different router) that you could try as a test? Maybe even take your iMac to a friend's house.
Finally - are you just curious to try the hardware test - or are you having an actual problem with hardware?