The said network adapter is not recognized in 13.04.
In 12.04 and 12.10 I had used the driver proposed from broadcom download site, configured as dkms package it was always updated.
On the 3.8.x kernels this provided kernel driver from broadcom does not compile anymore - and the distribution provided tg3 drivers does not recognize the ethernet adapter - even though it is a newer version.

~$ modinfo /lib/modules/3.8.0-19 generic/kernel/drivers/net/ethernet/broadcom/tg3.ko | grep -i version

version:        3.128

srcversion:     D737202366709FE01964BF0

vermagic:       3.8.0-19-generic SMP mod_unload modversions 

Here the working version on kernel 3.5.x using dkms

~$ modinfo /lib/modules/3.5.0-25-generic/updates/dkms/tg3.ko | grep version

version:        3.124c

srcversion:     D01ED9A7BF2C3956E212A63

vermagic:       3.5.0-25-generic SMP mod_unload modversions 

The Network card:

~$ lspci -nn | grep 0200

01:00.0 Ethernet controller [0200]: Broadcom Corporation NetXtreme BCM57766 Gigabit Ethernet PCIe [14e4:1686] (rev 01)

As found on the i7 Mac Mini 6,2.

Anyone knows where I can get a kernel that recognizes that ethernet device ?
That chip is supported somehow ...
And - the 3.8.x kernel is way better on the HD4000 chip - reason I use it.

Note - to get the WiFi working, just make sure you load the b43 driver at boot (/etc/modules). At least then you have Network connectivity.