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, they reset their clock back to 1904 and Ubuntu boots, but will 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.