Knoppix is well known to break after a hard disk install, and problems with networking may be the most common symptom. I have been seeing this for over for years now. You didn't say, but if it worked fine from CD then you have already demonstrated this. I urge you to try a distro like Debian that does not have this and other problems, but offers all of the software and features that Knoppix does.

While Knoppix has pppoe software to run your dsl connection without a router, I urge you to get one and operate safely (I'm assuming your dsl modem does not have one built in, you imply it does not). Even with only one computer you are much better off behind a NAT router, particularly if you ever run Windows.