I just spent an hour trying to access the forums when using Firefox 12. It does not display the bar with the New Your Stuff history etc. It updated itself yesterday or the day before and since then it is impossible to use on this forum.
I just had a thought and tried IE9 64 bit and it works OK. Loaded the same url on Firefox and the bar with the welcome username was not there.
It shows that I am logged in under the search box but still asks for me to log in. I even contacted Customer support, but they could not help.
So if you have problems accessing the forum, use a different browser.
According to your screen shot, you are not yet logged into Forums. There is a login/register link showing on the forums section of the page below the black Forums banner. The part of the page above the banner is served from adobe.com, the bottom part from forums.adobe.com. These are totally separate locations. Click on the Login / Register link and let us know if that fixes it.
I tried to log in on the page and it would not accept my password as I was already logged in to Adobe. A new password made no difference, it still would not accept the password and username. Logging in with IE9 was no problem.
Normally when I click on the adobe forums link on the Dreamweaver help I am sent to http://forums.adobe.com/community/dreamweaver?lang=en_US on my default browser - Mozilla. For some days now I have not been sent there, but arrive on the Adobe main page, and have to search for the forums using their search feature. Perhaps there was a crossed or broken link?
However, today for the first time for a while, it seems to be all working fine. I did report the problem to Mozilla, but whether they did anything I do not know at the moment.
I will see if this continues to work properly and report back.
Normally, if you are logged in at Adobe (upper right corner) and you click on the forums Login/Register link (upper left) it will just read the Adobe cookies, set a forum cookie, and let you in without ever showing the actual sign in page.
If you use the forum login/register link to sign in when not signed into Adobe.com that should sign you into both.