Again, sorry for being not clear but I did start this with a new profile original post: "Here is what I did so far: start from scratch with a new Thunderbird Profile...". I renamed the profiles.ini file to profiles.bak opened Thunderbird and thus started with a new profile. At that stage everything worked as expected, i.e. I could connect to the google account and add the calendars. When I tried to connect to my second (private) google account I couldn't connect and after that I couldn't connect to the other google account anymore.
At some point I did copy the mail directories from the original thunderbird profile to the new profile. I can't remember exactly if I did that before trying to connect to the second google account or before that. Could the mail folders have an effect on the connection to the google account? How can I further diagnose this?