Desktop PC is connected to the net but isnīt?

[Juud]

4 year old Dell PC, running XP, Windows Explorer (I know ), wireless connection.

When I look at the little wireless connection icon in the right bottom corner of the screen, it tells me:
Wireless network Connection
Speed: 54 Mbps
Signalstrength: excellent
Status: logged onto the net

But when I open Outlook Express, it tells me there is either a server or a network problem and that it can not log on.
When I start IE, it tells me that I am not logged onto the net and that it can not open the page.

I am writing this from the iBook, which works from the same wireless connection. Our landline phone is also via the net, and it works fine.
All usual lights are merrily blinking on the modem, and I have no idea what to do.
I have of course restarted the machine a few times, my Norton is up to date and I regularly run CrapCleaner and nCleaner.

Any Kind Boffin here who could take me by the hand and lead me through the streets of London?