Can't log in to iTunes Store

Strange kind of problem: When I start iTunes it connects, I can listen to the samples, I can download podcasts but I can not log into the store when for example I want to buy a song. I try, as usual, to log in with my AOL username and password, then iTunes says that it's connecting to the iTunes Store and then nothing happens - no error message whatsoever, it just connects and connects and connects.
The useless Apple customer support guy tells me something about firewalls etc and this would be a problem which they can not solve- but I have no firewalls activated.
I don't know any more what to do - does somebody know a solution?

MacMini Power PC G4
OSX 10.4.11
iTunes 7.6 (29)
I connect via AOL Phone Box to the internet, firewall is off...

Thanks in advance

mauermer