Which browser? I had a similar problem with Mozilla. After getting the Winmodem working via ltmodem, I configued the modem using KPPP so that it would dialup ok but Mozilla also has to be configured to my ISP username & password. It defaults to use the email address name for the username which is not correct so I had to reconfiguer it separately to the proper username.
I don't think there is any way to autologin as root but ther may be a way to autologin as 'user' i.e. as Knoppix. Maybe more experienced people will correct me on this.
You are not really supposed to be 'root' all the time anyway. It is more secure to login as a 'user' & su to root if you have to. Or use 'sudo'. Knoppix-on-HD by default doesn't allow any sudoers by default so you will have to edit the /etc/sudoers file to allow you as user (default 'Knoppix') to be a sudoer. I don't know why but there are a number of quirky little differencence like this between Knoppix-on-CD & Knoppix-onHD.