I'm a bit confused. Have you actually installed the driver, yet your NIC isn't recognized on boot? Or are you experiencing errors when you try to install the driver?
The abit link you provided is broken.
I think the driver you want is r8169, not r1000. This snippet is from the 2.6.20-rc2 kernel r8169 driver, and it appears to include support for your 8111b chip.
Code:
static const struct {
const char *name;
u8 mac_version;
u32 RxConfigMask; /* Clears the bits supported by this chip */
} rtl_chip_info[] = {
_R("RTL8169", RTL_GIGA_MAC_VER_01, 0xff7e1880),
_R("RTL8169s/8110s", RTL_GIGA_MAC_VER_02, 0xff7e1880),
_R("RTL8169s/8110s", RTL_GIGA_MAC_VER_03, 0xff7e1880),
_R("RTL8169sb/8110sb", RTL_GIGA_MAC_VER_04, 0xff7e1880),
_R("RTL8169sc/8110sc", RTL_GIGA_MAC_VER_05, 0xff7e1880),
_R("RTL8168b/8111b", RTL_GIGA_MAC_VER_11, 0xff7e1880), // PCI-E
_R("RTL8168b/8111b", RTL_GIGA_MAC_VER_12, 0xff7e1880), // PCI-E
_R("RTL8101e", RTL_GIGA_MAC_VER_13, 0xff7e1880), // PCI-E 8139
_R("RTL8100e", RTL_GIGA_MAC_VER_14, 0xff7e1880), // PCI-E 8139
_R("RTL8100e", RTL_GIGA_MAC_VER_15, 0xff7e1880) // PCI-E 8139
}