http://www.qbik.ch/usb/devices/showdevcat.php?id=16 will show you if your specific usb-to-ethernet card is supported.
If so, you need access to another linux based computer with all of the sources and developement stuff installed.
Then compile a kernel with the support for the usb-to-ethernet converter. It is unfortunate, but you are going to need the exact specs of the laptop and the chipsets within it for compiling a custom kernel which will fit on a single floppy. The kernel you create would be specific to the exact hardware in your laptop and you will want the networking support compiled into it as well.
This gives you a starting point for the linux on a floppy recovery/rescue disk.
which you can find by searching the net in google.com/linux.
Otherwise, you may have to blow $6-8 bucks on a serial cable specifically for connecting two computers together. If you have the cable, the directions for setting up that way are in the RedHat installation Guide. It is a pain in the butt, but it is do-able.