Well, to sign in on your laptop would be to check if you can log into ICQ using traditional means. Basically just to check that ICQ isn't down. So that would verify step one.

As for checking your password, having it log in automatically count. It means that the one you once upon a time typed into ICQ is correct, but not really that the one you typed into ICQ is the one you think you remember. Maybe you can log in on the icq2go web service on icq.com. If you successfully log in there, the username and password you're trying to use is correct.

For step three, you can attempt to download Pidgin from your application manager, and try ICQ there. If it works in Pidgin, chances are that there's some settings that's been keeping you from signing on.

So checking the settings you have on the N900 would be step four. Maybe ICQ changed their server or server port? Or worse, maybe they changed their protocol so that the N900 software isn't currently in a working state - I can't check that for you since my ICQ account is no longer available.