The LRP disk you made has support for some Ethernet cards like 3c509, 3c509b, ne2k-pci, etc., but if your LAN card does not match any of those modules you will have to add the support in the kernel for your card yourself.
Get the kernel module for the Ethernet card you are using on a separate floppy. (You can get this from a site such as Linux.com, redhat.com, etc., write it yourself or have it written for you by someone.) Insert this floppy into the floppy drive of your Linux router and mount the device using the command:
mount -t msdos /dev/fd0 /mnt
Copy the module to the modules directory of your Linux router, unmount the device, remove unneeded modules to save space and write your module name, as follows:
cp /mnt/rtl8139.o /lib/modules/. umount /mnt rm /lib/modules/3c509.o pico /etc/modules
Next, back up the changes and reboot. You may use the following if you want to avoid rebooting, but backup is necessary; otherwise, the changes will be lost the next time you have to reboot the Linux router: