The Gigibyte spec-sheet says the network is a Realtek 8201.

Googling suggests there's not a lot of documentation about this chipset, see for example:
http://www.matrixlist.com/pipermail/...ne/031523.html

<looks some more>
Some people are getting it going with the sis900 driver:-

eth0: Realtek RTL8201 PHY transceiver found at address 1.
eth0: Using transceiver found at address 1 as default
eth0: SiS 900 PCI Fast Ethernet at 0xd000, IRQ 10, 00:0a:e6:79:fc:fa.
eth0: Media Link On 100mbps full-duplex

Good luck...