hardware test disk image for 2008,24" iMac running 10.11.6

On those old models, the hardware test was located on disk 2 of the install media. I don't know of anything being available to download. Do you have your original install DVDs?

You can try getting the diagnostics from here:

https://github.com/upekkha/AppleHardwareTest

You should be able to use Disk Utility to "Restore" the .dmg image to a USB stick. The .dmg file should contain a .pdf file with the instructions, but if those instructions don't work, then you can use the instructions on the linked webpage.