I know the sub-page "BAM!" -> "Projects".
And I have found the "Sign-up" link. And also I know the "Find account" option.

The result for both projects is "Incorrect passwords". Of course - I use different passwords for different accounts.

I don't see how to insert a password for each project there. BAM only offers me to "Create Account" (but I still have accounts) and "Find account" (without asking for a password).

But what I do not understand why BAM tries to connect to my project accounts. There is no need.
The BOINC clients have the credentials for each account. Why not asking the BOINC client for project related data?

My BOINC client is logged in into BAM.

BAM! is based on using the same credentials for BAM! and all the BOINC projects. Only then you can use the nice features like Find Account, Sign Up and Create Account.