Do you have the latest Acrobat Pro X update? There were problems with communication with Windows OS (CNG) but I think they were fixed. Which Windows OS version do you have and which Acrobat X version (including minor)? When you say "the sign button in the "Sign Document" dialog does nothing", what really happens: You click on the "Sign" button and the dialog stays up, or the dialog goes away but you do not get "Save As" dialog and signature is not created, or you get "Save As" dialog but signature is not created? If this Acrobat X problem, it may not be fixed as it is close to its EOL.
I'm running Acrobat X Pro 10.1.15, which I believe is the latest patch. When I say the sign button does nothing, it does literally nothing. You click the button, and nothing happens. The sign dialog stays up, and you can repeatedly click "Sign" but nothing still happens. I've since looked into a bit deeper, and it seems that Adobe is having problems checking the revocation status. This has lead me to other suffering the same problem:
People report it still happens with Adobe Acrobat 11, so I'm going to try DC and see if it works like Adobe Reader DC does.
Just installed Acrobat Pro DC, and signing now works. On the revocation tab of the certificate details, it no longer performs a revocation check. It says this instead:
The selected certificate does not chain up to a certificate designated as a trusted anchor (see the Trust Tab for details). The result is that revocation checks were not performed on this certificate.
Acrobat has separate installation directories for different versions. What your last post tells me that you changed some settings in Acrobat XI installation and in Acrobat DC installation you may have gotten the default values. That's why signing "works" in DC but not XI. For instance, there is a preference (Security\cASPKI\cASPKI\cSign\iReqRevCheck) that controls revocation checking of the signing certificate. If it does not chain up to a trusted root then Acrobat will not use this certificate for signing. If your signing certificate does not chain up to the trusted root, as your latest post implies, then this could be the cause.