Okay, so you have a Broadcom 4318 [AirForce One 54g] 802.11g wireless chip! I'm pretty sure that indicates you need the (proprietary) Broadcom wl (small case WL) driver that is in the dot-pet I linked above in this Turbopup kernel.
I have an idea that it is the SSB module that might be causing problems and there was a post by tempestuous back during the Puppy 4.0~4.1 time-frame which addressed REMOVING SSB and blacklisting the stock b43 wireless driver. Let me do some searching (you can search, too) and we'll see if we can't resurrect those directions for this thread.
Give me a day or two.......
-Roy
EDIT: Found the following text file on my external hard drive....
So load the broadcom dot-pet into Turbopup & extract the firmware as mentioned in my first post, then go into /etc/rc.d/MODULESCONFIG and delete ssb:wl. You may also have to blacklist or remove b43 or b43 legacy, too. Save & reboot. You should then be able to load the wl driver if it is not showing up already.Dear all,
Important updates 4.2 final:
1. bcm43xx module problem
In 4.2 Final..bcm43xx is still being a problem...for those of you who wants a workaround..just edit /etc/rc.d/MODULESCONFIG (line 33) delete the <red word>
PREFLIST=' rt2500usb:rt73usb ath5k:ath_pci orinoco_nortel:hostap_plx orinoco_plx:hostap_plx orinoco_tmd:hostap_plx orinoco_pci:hostap_pci bcm43xx:wl b43:wl b43legacy:wl <ssb:wl> prism54:p54pci r8169:r8101 rtl8187:r8187 '
and reboot, make pup_save file when prompted, when puppy is booted again go to network wizard and bcm43xx won't be loaded