Looks as though the one screen shows your computer has found a 'self-assigned ISP' address that does not connect to anything; that's the number starting with 169.xxx. Not sure where the signal (strength) shown is coming from; you would need a wireless base station or router with an IP account to go online. You could use a wired connection using Ethernet cable, if you configure Network settings to use whatever paid service is available.
•Solutions for connecting to Internet, setting up small Network, and Troubleshooting:
•Creating a small Ethernet network:
•Resetting an AirPort base station FAQ
•Apple - Support - AirPort + Wi-Fi:
Given the portable computer you have appears to be an older one, and it may have
issue later trying to connect due to the security settings (WPA2, WEP, etc) you may
have to check the wireless system to be sure you have a matching security setting;
and if someone else owns the network, you'd have to get their password, too. Older
wi-fi systems use 802.11b/g/ and newer ones use a different wireless protocol; so
the old PowerBook G4 may need to use an old base station attached to the router
so it can use wireless internet; or just turn off the old web security, to see if it works.
Anyway, there are several things that could be going on in that situation, from the
settings, to the hardware. Plus whatever you may be using for a signal - source.
Oh, part of the issue, too, may be the very old OS X 10.2 (Jaguar) system. The
computer might* use as new an OS X as Leopard 10.5.8, that'd be a retail DVD
and a download of the last full step to get the (.8) part. Plus, some RAM may be
needed, too; so it could run OK. Not sure about the specs of your PowerBook.
If the PowerBook has a processor *slower than 867MHz, it can't run Leopard 10.5.
But the system itself will limit what you can connect the computer to, nowadays.
Good luck & happy computing!