Do you have another mac? Can you boot the problematic machine in Target Mode (boot holding the T key). Connect to the other mac and run system utilities (Disk, etc) from there.
What is the problem with your computer that requires you to run AHT?
Hope this helps.
The original AHT file is somewhat hidden.
The AHT is stuffed into an AHTxx.dmg file and found on the Recovery HD volume that is also hidden.
First you have to make the hidden partitions visible
To enable the see all partitions in Disk Utility (the Debug Menu)
defaults write com.apple.DiskUtility DUDebugMenuEnabled 1
In Disk utility now there will be a tab called Debug.
Use it to show hidden partition.
You will now see the Hidden partition called Recovery and EFI.
Mount the Recovery to see the files in finder and find the AHTxx.dmg
Delete it since it does not work anyway and it is a left over.
Now you can Disable the see all partitions in Disk utility (remove the Debug from the Tabs)
defaults write com.apple.DiskUtility DUDebugMenuEnabled 0
To Show all hidden files
defaults write com.apple.finder AppleShowAllFiles TRUE && killall Finder
When done replace the TRUE with FALSE to hide hidden files.
Try the Diagnostic mode.
Since you do not have one anymore, the Internet version should come up automagicaly.
Best Answer
There could be a whole range of reasons you're unable to get this to work (e.g. problems with your optical drive; a problem with your disks, etc), so it may be worth downloading AHT directly from Apple and running it from a USB.
NOTE: By following steps 1 and 2 above you have already done the first and third bullet points on the github page.
Let me know how you go.