No, you don't have to remove all Adobe programs to update Reader.
What is the name of the key that cannot be opened?
The key is:
I eventually got help from a Microsoft Enginneer. He used a small MS system utility ( the name escapes me, but I think it was subinacl.exe) which went through my registry.
It corrected several permissions problems in my registry. I suspect some rogue software I installed screwed them up very badly.
Anyway, after that & ever since, everything installed and ran perfectly.
All other solutions and "registry fix" programs from third parties were completely useless.
I'm glad your issue was resolved.
My post is to state that editing the registry, especially for permissions, should not be suggested for this issue. Its important to understand that, for these 1402/1406 errors, the issue is with the installer and not the operating system. In any event, I have updated my document to include the submittal of the bug to Adobe and have included information on how to correct this prior to installation for advanced users (more likely, system administrators or software packagers).