I'd guess that the EEPROM contains some information about how the chipset is connected together, to the rest of the machine, and to the ethernet jack, meaning that you have to find an identical device, not just another e1000e, and putting something plausible but wrong could make it do further damage. (In particular, I wouldn't be too surprised if the device checks the eeprom checksum, if that's okay, initializes the PHY, and waits for that before setting up PCI bus interactions; if the checksum is good but the PHY info is wrong, it'll wait forever.)