Problem "solved"
It was suggested to me that perhaps CB was not to be blamed, but the problem could be because of the sum of memory taken up by other moduls as well as CB.
However, Community Builder is the only non native extension that I have installed
Components
Banners
Community Builder
Mass Mail
News Feeds
Polls
Syndicate
Web Links
Modules
mod_cbloginrc2
mod_comprofilermoderator
mod_comprofileronline
mod_mainmenu
mod_mostread
mod_newsflash
mod_poll Site
mod_random_image
mod_related_items
mod_search
mod_stats
mod_templatechooser
mod_whosonline Site
mod_wrapper
mod_latest
mod_logged
mod_popular
mod_stats
But, then the advice turned out to be really useful to me. I turned off all other modules, such as "polls", "newsflash", latest news", etc, down to the bare bone.
And, now it works! I can click and see the CB profiles.
I'm running this on a free server at the moment, just for testing. When I get a "proper" server, I will probably have more memory, so if my tests show that the users should have CB, then I can give it to them.
I guess 8MB is very little...??
Best regards, and thank you all for the way you contribute, it's great ... maybe the world is a good place after all
Lars