It used to work fine on Windows 8 but after the update to Windows 8.1 it always started the registration wizard for a new activation. Unfortunately this activation did not work, I tried it twice, just to be sure. So, again I turned to the Google and found Code Singh: Virtualising Delphi 6 PC (Activation Errors)
The problem described there looked a lot like the one I was having so since I had nothing to lose, I just deleted the registry entry
(I did not make a backup, what would have been the point?)
I started Delphi 6, ignored the warning about incompatibilities (which was talking about Delphi 7 anyway) and went through the registration/activation process again. This time it worked.
Maybe I should mention, that I did not install any of my Delphi versions to c:\program files but put them into c:\Delphi instead to avoid any problems with access rights to the installation directory.
So, now I have got working Installations of Delphi 6 to XE4 again.
XE3 and XE5 are missing, but I hope that’s just a matter of installing them.