AHT and Apple Diagnostics not working!
You will need the exact model information,
not just as you say pre-2013

then we can help you looking to download the correct AHT for your model on the web (if it exists), since the AHT are model specific.

From the screen shot you can see it is a:

MacBook Pro (15 inch, Mid 2010) (MacBookPro6,2/Mac-F22586C8)

Using the above information now we have to find the unique Model Number identifier for the AHT file. 

There is no method or listing for that just plain web search.

Getting the AHT is sort of back door in to Apple support.

&gt; http://download.info.apple.com/Apple_Hardware_Test/018-[MODEL
&gt; NUMBER]-A.dmg


UPDATE 

I did some searching for you and, I found it:

Mac-F22586C8, MacBookPro6,2 

022-4597-A.dmg

Enter that in the above link.

Let me know if I got the right file for my records.

More Update:

There is also a very nice database containing Apple Hardware Diagnostics files, all you need is your Model Identifier (found in About this Mac.