I wanted to post the following "instructions" in case they'd be of use to anyone else.
My new hard drive came today (80GB Hitachi Deskstar SATA) and I was able to image the old parallel IDE drive to the new one without a hitch. Just to be clear, what I wanted to end up with was the new drive exactly replacing the old one, but with more space. I may try to use the old one as a secondary drive later, but not right away.
Here's what I did (expanding on these Instructions)
1) Installed the SATA drivers for my Motherboard (K8T-NEO FSR) into Windows.
2) Burnt the latest Knoppix Linux-on-CD (3.4) to disc.
3) Rebooted with the CD in the drive. Gave it the "knoppix26 lang=us" start option. If you go with the default, you get the 2.4 Kernel and it won't support SATA.
4) Opened the root shell and unmounted the C: drive ' umount /mnt/hda1'. Double-checked that this worked by running 'mount' and verifying neither hda nor hdg (the device assigned to my Sata drive) appeared. BTW, I didn't expect it to be /hdg. I only noticed the name during the boot sequence.
5) From the root shell, I ran 'dd if=/dev/hda of=/dev/hdg'. That basically says, copy every byte from /dev/hda to /dev/hdg. This took about an hour to do 20GB. You can check on the process while it's running by doing a 'kill -SIGUSR1 <pid of the dd process>'. If you don't know Unix, don't worry about it. Just be patient. For reference, I was getting about a 9MB/s transfer rate.
6) At this point, the new drive is exactly like the old one, plus a bunch of unusable wasted space. To enlarge the 20GB partition to 80GB, I used QtParted (partition editor) which comes with Knoppix.
7) I disconnected the old IDE drive and then had to tell my BIOS to use the SATA drive at boot time.