Drupal itself has not gotten it to work properly?

yesterday I tried to login to the user group drupal site. To no avail, it kept simply referring me back to the login page over and over again.
To make sure that it is not a flaw with my username, I bothered and registered for a new account there [new name, new email address], still could not login either, was "advised to send another request for a different password.
Then I tried to use the new user information from the registration and sign in to the drupal org site - also to no avail, simply says: wrong username or pw.

I desperately need such module because I have ten sites [10 different domains] where Drupal is on and need users to be able to use the same login info on any site.

I can not install Drupal without knowing if this will actually work since this is a pre-requisite for running the sites. I chose Drupal for specific known reasons to be the cms - but this is definitely a stumbling block.

Would very much appreciate appropriate info about this and a solution if there is one.
I am on linux server, all domains are hosted on the same server but with individual DB's.
Thanks.
Michele