Same here
iBook G4 12"... same thing... will run for a few minutes, but then it freezes up. Still have everything on the screen.
Some interesting notes.. it started the day after I got a battery from the Apple replacement program. I put in the battery, used it for an hour or so until it was almost dead, powered off, and plugged it in until it was charged.. removed plug.. and let it sit overnight (I went to sleep). Woke up next day, powered on, grabbed a coffee, and when I went to login it was frozen. Held power till reboot, logged in, opened browser, and opened webpage... then it froze. Rebooted again, it didnt goto login screen, went to a flat blue screen. Over and over and over. I finally popped the keyboard off, removed the aircard and the extra stick of RAM (both since computer was new). Now it will boot up almost every time, but will totally freeze after 1-10 minutes or so. Everytime. No video issues, just system lockup.
I also noticed that if you boot to command prompt, it will stay on longer, but eventually will crash out and go to a black screen. Since even command mode freezes or crashes out, it must be hardware, but since there does not seem to be any video issues, I dont even know what to look for.
Oh, and, I have my hardware test CD, it ran through without crashing and said everything passed
Update - next day - I have been trying to get all files off this iBook, could not target disk b/c was ile vaulted... could not turn off file vault b/c 1. not enough disk space 2. not enough time before crash. I have been going in, copying files out of home into shared until crash, then target disk to new macbook, go back delete and move more files. Got all off, then was able to finally turn off file vault... AND IT HAS NOT CRASHED SINCE. Slept all night, been on for about 2hrs now without freezing up. Was it file vault all along?