If I try to find my WCG account via the "Sign-up for projects" page (http://boincstats.com/bam/project_sign_up.php), I got the following error:

"Checking for existing account at World Community Grid -> No response from project"

WCG Username == BAM Username
Password == BAM Password

No BAM problem, WCG has server problems recently, see for example here.
You could have find that by a bit searching before posting...

I have found this thread. But nothing in there is explaining this issue.
Because I do not have any problems "with signing into the website or having the BOINC agent communicate with the servers" or "which made the website and BOINC grid unavailable for about 4 hours".

Since 22.01.2009 I'm continously trying to get this done - without success. So I thougth it might be a bug...

You aren't the only one having this problem:

WCG not connecting to my BAM??!!

Sadly, there hasn't been a solution/total explanation yet... WCG has had problems with BAM! for quite some time--when I added WCG to BAM! a while ago it took a few tries, but it eventually worked. Apparently, some people now can't get it to go at all. One explanation for the problems I've heard is that they are caused by the custom software that WCG is using, which is quite a bit different from that used by other projects.

You could do a work-around by attaching to the project manually until this is resolved, but keep trying--maybe you'll do it when the planets are aligned correctly.

Haha, in response to the "but keep trying--maybe you'll do it when the planets are aligned correctly" I tried for the 1000th time or so, and suddenly it worked

Nice! It worked here too!
Finally!