Hi yes
04:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168B PCI Express Gigabit Ethernet controller [10ec:8168] (rev 06)
Subsystem: ASRock Incorporation Motherboard (one of many) [1849:8168]
Kernel driver in use: r8168
Kernel modules: r8169, r8168
Is that what you are after.
Yes, that was! We are testing a new kernel that should properly support your card using the r8169 module.
Thanks. 
AS
Works fine with 2.6.38.8-pclos1.bfs default install kernel, as well as the 2.6.38.8-pclos3.bfs and 2.6.38.8-pclos3.pae.bfs kernels now.
From my computer:
03:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8111/8168B PCI Express Gigabit Ethernet controller [10ec:8168] (rev 06)
Subsystem: Giga-byte Technology GA-EP45-DS5 Motherboard [1458:e000]
Kernel driver in use: r8169
Kernel modules: r8169
Also works properly with every Kernel I can test back to the upgraded 2007 pre release TR4 with a 2.6.22.15.tex3 kernel. The original installed kernel on that installation is 2.6.18.8.tex5, but I seem to have deleted the menu.lst stanza for that kernel.
The point being there is no kernel I can readily access on any installation on this machine (12 total, presently, ranging from 2007 to the current image installation) that doesn't work correctly with the
supplied default modules for this controller.
Whatever the problem
RathB5 is having, it is local to his machine, not a general problem of the supplied default modules.