02:00.0 Network controller [0280]: Broadcom Corporation BCM4313 802.11b/g LP-PHY [14e4:4727] (rev 01)
Subsystem: Askey Computer Corp. Device [144f:7179]
Right - you don't have a driver for that hardware.
14e4:4727 - -is the PCI ID
For example this line is he driver for the WIRED enet
Next question - is there a driver, is it in a later kernel.
Here is a proprietary driver for Linux, you can google up directions for building & installing
http://www.broadcom.com/support/802.11/linux_sta.php
However there IS a driver for the 4313 in recent Linux kernels.
brcmfmac.ko or maybe brcmutil.ko
but these didn't exist until very recent kernels.
If I were you I'd install f16 and then install a new kernel from koji. Trying to make new harware play under old software is a time-waster.
---------- Post added at 10:54 AM ---------- Previous post was at 10:49 AM ----------
That driver was added to the kernel on October 11, 2011, and ARE in the F16 standard kernel (koji not required).
/lib/modules/3.2.6-3.fc16.x86_64/backports/drivers/net/wireless/brcm80211/brcmfmac/brcmfmac.ko
/lib/modules/3.2.7-1.fc16.x86_64/backports/drivers/net/wireless/brcm80211/brcmfmac/brcmfmac.ko
/lib/modules/3.2.9-1.fc16.x86_64/backports/drivers/net/wireless/brcm80211/brcmfmac/brcmfmac.ko
/lib/modules/3.2.6-3.fc16.x86_64/backports/drivers/net/wireless/brcm80211/brcmutil/brcmutil.ko
/lib/modules/3.2.7-1.fc16.x86_64/backports/drivers/net/wireless/brcm80211/brcmutil/brcmutil.ko
/lib/modules/3.2.9-1.fc16.x86_64/backports/drivers/net/wireless/brcm80211/brcmutil/brcmutil.ko
Install F16 ! Reboot.