Have you tried to download and install the patch for CS6?
Have you tried to reset preferences?
@ Michael Witherell thanks for your reply. My InDesign is up to date in Help / Updates (if that is what you mean by the patch) and yes I have reset the preferences but the problem is the same - touching the select tool is enough to cause a crash. While searching on InDesign crashing I saw a suggestion to create a new user in Windows. I don't want to speak too soon but this seems to fix the problem - with my regular Windows user (in which I do everything inlcluding CS6 Photoshop) and with no other programs running, using the select tool (for example) immediately causes InDesign to crash but with the new user it seems so far that I can use the select tool - move stuff around - with no crashing so far. Does that give any clue to what the problem is?
That means the problem is in the user profile.
You said you reset the prefs, but let's be sure you did it right. See Replace Your Preferences. You need to be logged in on the account that has the problem to use the Keyboard method.
If that doesn't work, reboot, log in with the user that has the problem and rename the Adobe folders from the AppData\Local\ and AppData\Roaming\ sections of your user, to _adobe, the copy the folders from the same locations in the profile of the working user and paste them into the profile with the problem.