Trouble adding Powerbook to network

I just inherited a 15" Powerbook G4, and I have a mini current gen. When I start the powerbook, it finds my Airport network, asks me for the password which I put in, and it says it's connected. I can also see the mini and my shared folder in Networks, so I know the powerbook is on the network. When I open Safari, it can't load a page. I run Network Diagnostics, and it gets to the point where it asks if I'm using a DSL or cable modem (I am) and it tells me to reset the device (the modem?), which I do, but it still won't work. What am I doing wrong? I don't understand why, if I'm connected to my network, I can't get online. Am I supposed to be restarting my mini when I reset the modem?

Also, on the powerbook, when I try and unlock the little lock in Network Prefs, etc., it asks for my admin name and password. I put in my user name and password, and I get an error message. It let me change my password, so I know it's right. Is it possible that my admin name is not my user name? If so, is there a way to find out the admin name, because I know the password! I'm looking for my OS X disc, to do a reinstall, if necessary.

Thanks for the help!

Well, I have the Powerbook's original discs, but they are OS 10.3, but the computer has been updated to 10.5. So the mini restore disc, which has 10.5 on it, won't work for the Powerbook? Would I have to buy a copy of Leopard? I'm assuming my uncle (who owned the computer before) bought Leopard at some point, so maybe he has the disc? Argh.

And there was obviously a pretty clean reinstall done, because everything is like new. My uncle set up a user account with my name, but it doesn't seem to be the admin name. If that's possible.

Just wanted to add that I have an Airport Express hooked up to my stereo and my printer. Wasn't sure if that would interfere at all, such as I would connect to that and not to the mini's Airport?
I also had similar problems a week or so ago trying to get a PC onto my network. Not sure what the heck I'm doing wrong. Maybe security or something?!?!