Well after googling it, and translating quite a few pages
it seems there is a means to use Firewire to transfer the video. However, if serial truly is your only choice, when you plug in the camcorder (after knoppix is all booted) and turn it on (in VCR mode), does dmesg tell you anything about what's going on? Is there any info at all about the connected camcorder?
You may be in the boat of having to get some time of 'serial to usb' converter, or something along those lines. I'm really amazed that they would use serial to transfer video though, seems a bit... slow. Another option might be to get a device that reads DV tapes and actually has Firewire or USB2 on it (such as a newer DV camcorder). If you have a lot of tapes, I know there are some on-site facilities in my neck of the woods where you can send them the tapes and they'll transfer them to DVD for you (or any other medium really).