Ok, new install, it didn't work from the beginning, same problem with the 403 error HOWEVER, I've disabled sh404SEF component (from within the component itelf I've choosen the option Use=NO) and IT WORKED the login in CB.

At the time I've done that the configuration in Joomla was this:

Search Engine Friendly URLs: NO
Use Apache mod_rewrite: YES

and

Allow User Registration: NO
New User Account Activation: YES

(Note: all CB settings as per installation guide).

Happy now I've enabled again sh404SEF and believe or not IT WORKED AS WELL.

Not sure at this moment in time what went wrong but now CB is behaving as expected on my site.
I cannot say for sure if the sh404SEF component caused any troubles but the installation of CB went fine from the beginning on a sub-domain of my site (also tryied a fresh install in this sub-domain and everything was ok) on which I'm not using sh404SEF.

Makes sense. Purge all shSEFurl's and let them be recreated. First check all menu's and menu trash to ensure there are no linging links to com_comprofiler