I have the same problem on a Dell Precision 390. I have two ethernet cards, one broadcom integrated on the motherboard and an other broadcom separated. The card that isn't integrated with the motherboard works good after the installation of RHEL 4 (without any additional driver). But the integrated doesn't work, so we built and installed the latest tg3 broadcom driver with the same procedure quoted in this post (rpmbuild -bb work well for us :)). But unfortunatly, the ethernet card still unrecognized and it doesn't fix the problem.

SUSE 10.1 drivers
 

College I'm at has the same NICs (57xx netXtreme gigabit controller) in Dell machines, and they aren't being seen by SUSE 10.1 (they're fine with XP so the NICs are ok).

Broadcom advises the tg3 linux driver, but said also it would need to be compiled (compile the kernel). I'm just a student there so I'm not sure what the IT dept has already tried, I doubt they'd want to be recompiling the whole kernel though -

does anyone know if there's updates for SUSE 10.1 that already recognise the Broadcom NIC? So the whole kernel doesn't need recompiled - I don't know if they can do all the machines at once over the network, but our linux class apparently needs SUSE to do ftp and web server practicals - we have telnet access to a network (CLI only) version of linux, but I don't know whether or not we can use it for that part of the class.
We don't need wireless to work on the NICs, just wired.

Or it might be that some of the other drivers work?