The BCM5705 is a member of the Broadcom Tigon 3 Gigabit card chipset family, the module exists in 2.4.22, which is what I think Fedora shipped with, so you should have it onboard, what happens when you:
Now, the wireless network adapter isn't covered, blame it all on Intel and their not releasing enough specs. There is hope though, there is a kernel driver that wraps for the Windows drivers. The commercial one can be had from:
For a 30-day trial and then a $20 license, or there's the slightly more complicated free one:
Now, the Fedora Core 2 kernel is just a newer kernel then what you've got onboard, it should work, if you just grab the kernel RPM and try to install it, probably with the --force option, but I wouldn't recommend it. Its much easier and safer to compile a 2.4.25 by hand, that has onboard the tg3.o module for your card. From what I've read, the driver is a bit buggy in 100baseT mode, but that's since been resolved in newer kernels.