The good news is that you're still under warranty. The bad news is that you may have to use it.
What does is say on the screen just before the crash? Is there a particular service starting when it crashes? How does it crash? Turns off? Tells you to restart? Unresponsive?
Here's the voodoo you try when you get an odd problem--and this is an odd problem. Start your Mac while holding down command option P R and hold them until you've heard the startup sound 4 times. Then hold command option O F until the text on the screen tells you to let go. Type reset-nvram and hit enter. Then type reset-all and hit enter again. The computer will reboot and will have all it's hardware reset. It may work or it may not. If you have a bona fide "broken hardware" problem it won't do anything, but there's no harm in trying.
You might try reinstalling the OS as well, but my gut instinct tells me that's not the answer. Again, it won't hurt to try.
Your first priority should be backing up your data.
EDIT: Run the hardware diagnostic CD that came with your iBook.