I've tried hooking up a basic USB cable, but the current iBook doesn't recognize the old iMac.

Instead of using a cable use a usb flash stick formatted to fat 32. Drag diles onto the USB from the old computer then you can move them onto the new one. If the old mac is an OS 9 you may want to add extensions to the files to help them be recognized by the applications to open this can be done after the file is moved.