For Windows networking (the file sharing stuff) to work, your Ubuntu box has to be able to determine an "address" for the Windows box. There are various methods samba uses to determine the address. All of these methods take a name (BILLY in your case) and output a location.
To determine if the problem is finding an address for the computer, type this on the prompt:
smbclient -L BILLY
If you get output like you flooded the channel with earlier, it works. That output was a list of shares on the computer BILLY. That's what you want to see. If that command works, forget this information.
If it doesn't work, try:
smbclient -R bcast BILLY
If that works, we've found the problem.
In /etc/samba/smb.conf find the line that reads:
; name resolve order = lmhosts host wins bcast
Change it to read:
name resolve order = bcast
Now again try:
smbclient -L BILLY
If it works you've fixed the problem. The only way I could find to get Nautilus (the Ubuntu file explorer) to read the new settings was to reboot the computer. After reboot, see if you can browse your windows box.