Don't think serial connection can be of any help to you. It doesn't allow you to do much with the box. It is mostly to rescue the box when something is damaged and can't be flashed. Like repair boot or something like that or change boot procedure.
Although you might use it for diagnosing the problem. Maybe it might suggest what is wrong and maybe help toward a solution.
But I don't know what the settings should be to connect to your box. For dreambox I think they are:
115200,8,n,1,Xon/Xoff
You use hyper terminal, and create new connection and choose connect using COM1 configured with values mentioned above. You connect serial cable from your pc to the stb and see if you get anything on hyperterminal once you reboot the box.