Either I'm getting confused, or you are changing the equipment on me.
Your pictures show the Computer Named "MacBookPro" as having internet sharing enabled. I was under the impression that you were going to attach the USB antenna to the Powerbook G4, which would then share the neighbor's ISP connection?
Did you switch equipment, or is your Powerbook G4 named "MacBookPro"?
If the MacBook Pro is the Mac at the end of the line, it should NOT be setup as internet sharing. It should just be an ordinary client.
Again, going on the prior information.
USB Antenna picks up neighbor's WiFi signal.
USB Antenna is connected to Powerbook G4
Powerbook G4 -> System Preferences -> Sharing -> Internet Sharing -> Share your connection from: USB Antenna (whatever name that takes on).
Powerbook G4 -> System Preferences -> Sharing -> Internet Sharing -> To computers using: Ethernet
Ethernet cable from Powerbook G4 to Linksys router's WAN port. This might have "WAN" labeled on it, it might have "Internet" labeled on it. I guess it could have "Modem". But no matter what it should be separate from the 4 switched ports either with some physical distance, or a different colored plastic.
The Linksys router should then pick up an IP address from the Powerbook G4's Ethernet as the Powerbook G4 Ethernet is suppose to be acting as a router providing typical DHCP and NAT services to anything connected to the Powerbook G4's Ethernet cable. The typical Mac OS X Internet Sharing IP addresses are 192.168.0.n
The Linksys should then share the Powerbook G4's Ethernet connection via both its WiFi transmitter, and its 4 switched Ethernet ports. Since the Linksys is sharing its WAN port, it will implement its own DHCP and NAT services on its WiFi and 4 switched Ethernet ports. The IP addresses assigned by the Linksys would be the typical 192.168.1.n IP address range.
NOTICE that the Mac OS X Internet Sharing subnet is 192.168.0.n where as the typical Linksys subnet is 192.168.1.n
Alternative 1) You may choose to eliminate the Linksys altogether. That would be by telling the Powerbook G4 to share the internet connection via your Powerbook G4's Airport card. Now your Powerbook G4 is a WiFi base station and your MacBook Pro should be able to connect to it just as if you were in a WiFi hotspot.
Powerbook G4 -> System Preferences -> Sharing -> Internet Sharing ->To computers using: Airport
Again, the IP address range assigned by the Powerbook G4 acting as a WiFi hotspot would be 192.168.0.n, and the MacBook Pro should get an address in this range.
Alternative 2) Going back to sharing via Ethernet, you could choose to connect your MacBook Pro directly to the Powerbook G4's Ethernet cable. This does limit your mobility. In this case again, you MacBook Pro should pick up a 192.168.0.n IP address.
Alternative 3) Again going with sharing via Ethernet, you decide to connect the Linksys via one of the 4 switch ports (NOT the WAN port, or whatever it is labeled). In this case you must configure the Linksys to "Disable" DHCP. There should be a "Disable" button on the Linksys DHCP configure page. Or an "On" / "Off" button, or something that indicates whether the Linksys is to provide DHCP addresses. Once you turn off the Linksys DHCP services, it should just turn into a glorified swtich and Ethernet to WiFi bridge device. Once in this Bridge mode, the Powerbook G4's DHCP server should be assigning 192.168.0.n IP addresses to anything connecting via the Linksys. The Linksys itself will NOT acquire its own address as it is no longer acting as a router, but just a "Bridge" and a Bridge does not need an IP address.
If you are getting assigned the correct IP addressed for the configuration you decide to try, and you still can not access the internet from your MacBook Pro, then look to see if you have working DNS server addresses. you can always plug in your own DNS addresses on your MacBook Pro using
MacBook Pro -> System Preferences -> Internet -> Advanced -> DNS -> +
Then enter something like the OpenDNS server addresses or the Google DNS server addresses
OpenDNS.org
208.67.222.222
208.67.220.220
Google DNS
8.8.8.8
8.8.4.4
Final option. Pitch a tent in your neighbor's back yard, and live their until you get your own internet service :-)