Johnny Cakes was right about the program file. It's a directory buried within the Adobe program directory in the Program Files (x86) directory. Check these two out:
c:\Program Files (x86)\Adobe\Acrobat 10.0\
c:\Program Files (x86)\Adobe\Acrobat 10.0\Acrobat\
The directory it's in is called "GC," and the file name is "AdobeGCClient.exe" and there could also be a file name called "AdobeGCUpdater.dll." I even found a file named "dispatchtable.xml" there as well.
DELETE THE ENTIRE DIRECTORY!
The registry key where I found "AdobeGCClient.exe" was called:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Installer\UserData\S-1-5-18\Components\1B8DC4840EADDB343B2D25158713B3C0\68AB67CA330100007706000000000050
however, you'll probably want to do a search on the "AdobeGCClient.exe" file name because it could be a slightly different location.
DELETE THIS ENTIRE ENTRY
Sorry this took so long. I realized just this morning that this offending program could also be on my laptop computer which also has Acrobat 10 on it. When I searched for it I found it and copied this information to share with you all.
ShadowAce, I wanted to get this to you too so you could get it out to everyone on your ping list.
Thanks for your patience!
Many thanks for the solution to a real problem, and the precisely detailed instructions.
In addition, I have opened Acrobat X Pro and went to Edit > Preferences > Updater and put a tick in the last option to prevent automatic updating from causing the same problem to reappear through that open door that the application uses to “call home” to Adobe corporate. Adobe is IMO the unethical inventor of this problem that is a ploy to sell the “fix” that is an “upgrade” to their subscription service. I believe Adobe is simply blacklisting bona fide serials on their older permanent license software to force “upgrades” to be made to their subscription service Acrobat DC version. It is a greed motivated “security alert” that your Acrobat is not genuine more than a fact, IMO.