I am not sure that the MMRE driver is correct for the 8139C, although it *may* be selected by the installer. The MMRE driver is for gigabit NICs, while the 8139 series is 10/100 Mbs. I am pretty sure that the RTSND driver will work with the 8139C. Use NAPS (System Setup-> Network-> adapters and Protocols), to change the driver.
I will remind people, that MMRE is the new, on going, driver for Realtek Gbs NICs. You should NEVER use the ancient R8168 driver, because it can do some nasty tricks, like disable the NIC, until the machine is totally powered down (pull the plug). Even windows, and Linux, failed to turn it back on, for me. I have one realtek NIC that will do some very strange things with the R8169 driver, but all of the Realtek Gbs NICs, that I have, work with the MMRE driver. Strangely, MMRE does claim to support a couple of 8139 10/100 Mbs chips, but I am not so sure that it actually does (I haven't tried it myself).
It would be interesting to know if the old drivers can be installed in arcaos?
Any driver should work with ArcaOS, if it is designed to work with warp 4. Whether it will work any better than what is supplied with ArcaOS is highly unlikely, but not impossible.