Have you checked the shortcut set you are using to see if it's really enabled?
Yes. I checked everything I could check. Verified every setting. Nothing helped.
At the moment I'm uninstalling the program, after that I'm gonna use the Clean Tool to be sure everything got deleted, and I'll reinstall everything back. Hope that will fix the issues.
Does it work in a different user account or if you start up in Safe Mode?
No. But I think I figured it out somehow.
I just reinstalled the InDesign CS6 from scratch, as mentioned in the post above. Everything as new as possible. And it still had problems. Then I disabled two things from autostarting:
Broadcom 802.11 Network Adapter Wireless Network Tray Applet
Logitech SetPoint driver.
After that, everything went back to normal.
I assume one of them had grabbed the hotkey without mentioning it, so that must have been the fault. I don't think that other programs (other than Adobe's) have the same key bindings as InDesign.
P.S.: Just restarted each disabled program and it's the Broadcom 802.11 Network Adapter Wireless Network Tray Applet that shows issues with the keys.
So, thanks for trying to help me fix my problem.
If anybody else have troubles with the keys and they have this specific tray applet running, better disable it to be sure. In Windows Task Manager it is called WLTRAY.EXE.