OK, I just want to be sure we're talking about the same thing here. It's entirely possible that there's something different with your setup somehow. Since a picture is worth a thousand words, here are 3,000 words :)
This is what I see when I click on your name in the post above this one. I'd be able to start a conversation with you by clicking on that option.
This is what I see when I hover over my name up in the upper right corner. The second item down on the right column is where you can see your conversations and start a new one.
And this, finally, is at the top of the page after I click on the Conversations menu item in the previous image. You can start a new conversation by clicking on the big green button on the right hand side.
Now you may not be seeing this, I just wanted us both to be on the same sheet of music while it's being discussed :)
Thanks for letting me be so wordy.