The iBook did not respond to PRAM, PMU or any other resetting, neither did it respond to any key combination. I found this thread somewhere
http://www.powerbookcentral.com/clas.../t/001238.html where some guy had the exact same problem, and by letting the mac "rest" for a couple of hours without the battery, and restarting after that time, he got it to work.
I don't think it is a screen issue, as I could start it once for some minutes, and got to send an email before it froze. Do you think it is the logic board that's failing?
Thank you very much for your concern.