The driver in the boot-floppies images for the eepro100 seems to be out-of-date and broken. The problem is characterized by the NIC's failure to respond after minimal usage. Intel (and newer drivers for the NIC) offers a working driver for Linux that I have successfully tested under Slackware 7.1. The driver source can be found by following link #2 below. Link #1 indicates the URL of the boot-floppies page with the boot images with the broken driver (phew!).
1. http://people.debian.org/~dwhedon/boot-floppies/
2. http://support.intel.com/support/network/adapter/index.htm
Dan