I have tried a Realtek 8139 and Realtek 8111 NIC on my 12.04 Ubuntu desktop machine. Neither will operate at 1000BaseT when I try to force it with ethtool.
I have the exact same issue and unfortunately, no one but you and I seem to recognize this is the problem behind the "slow wired connection" problems in all the blogs.
I have not found a solution other than plugging it into a 100Mb switch instead of a gigabit switch and running at 100 full duplex.
You can add to
EDIT: Found a solution!!!
You can download and install an updated driver from this link
I am now (finally) at gigabit.