Ibook

We have two dual-USB iBooks running Ubuntu.

http://support.apple.com/specs/ibook/iBook_Dual_USB.html

When the main battery is disconnected or fully discharged, they reset their clock back to 1904. This causes Ubuntu to boot, but not allow anyone to log in. The workaround is to log in with a fail-safe session and set the clock to a reasonable date and then log out and log in with a normal session.

I suspect there is a smaller watch battery somewhere in there that should be keeping the time but that it is dead after all these years.