I do not see any reason why the broadcom driver must not work.
Do you have any other system where you can download the broadcom drivers from internet ? you
can then copy the source to the linux machine and install the drivers. This is supposed to work
Looking at the broadcom site, it clearly says the driver is tg3 whereas you are reporting that tg3 is
not working. The next alternative i would try is
1. To rmmod tg3 and modprobe again to find out in dmesg what are the messages shown which would give us a
clue on what is happening.
2. To download the new tg3 driver from broadcom and have it installed. You will need kernel source packages
and some experience of having compiled binaries from source. [ surely a second option ]