Thanks for checking this all, you still did not mentioned if you are using a WIN 64 7, 8 or 10 ?
but anyway this VST path is quite uncommon, it is reported on Ableton web site that using some system
folders could cause issue with loading Vst's.
Check those links by them for further trouble shooting
But for now could you please try the following :
1- Create a new VST folder path C:\Program Files\Vstplugins\
and move the A.N.Ax64.dll in the Vstplugins folder so you end up with
2- Once you are sure your A.N.Ax64.dll is only there and not in your previous desktop vst folder,
open up Live 9 and change your custom VST folder in the options/files from Live then do a rescan or
This will isolate the ANA x64.dll file in order to see if it's working under that new path, and if it is then I suggest you to copy/move all your plugins under that new path.
If it's not solving the problem, you can set back your custom VST folder as it was before in your Live preferences, you won't loose anything, just be aware that if you have a huge number of plugins, Live will take some time to rescan them all.
But it's a good way to isolate the A.N.Ax64.dll to trouble shoot your issue.
Also, you may want to be sure that your ANA 1.5 demo was not corrupted from download or extraction of the archive, because those things can happen, it could worth it to try a new download and a clean new install.
Let me know if the .dll file works in the new VST path.