I did not get any help. So I had to try a lot of things, to make it work.
So perhaps this helps some others if they have the same problem.
I had comprofiler_online on position user6, because I used ja_t3_blank with this position.
Changing to all other templates (beez, coolness, mycommunity, rhuk_milkyway). it was never a problem.
With funlite I got blank page, even no debug informations.
Only now with nearly all plugins disabled I got the information:
Fatal error: Cannot redeclare getnameformatonline() (previously declared in /srv/www/vhosts/mysite.ch/httpdocs/modules/mod_comprofileronline/mod_comprofileronline.php:37) in /srv/www/vhosts/mysite.ch/httpdocs/modules/mod_comprofileronline/mod_comprofileronline.php on line 56
When I disabled now this module (or changed the position) the template works.