Hibernating itself uses no power at all. All of the RAM contents are written to the hard drive then read back in on the next boot.
The problem could be that some motherboards keep external devices powered constantly. A common one is the keyboard and mouse (this is so that the computer can be started by using a keyboard/mouse button rather than the case button). Have a look at the BIOS and there might be a setting like "Keyboard Power-On" or similar.
Otherwise you might just have to install a timed relay switch which actually cuts power after the car is stopped. Or a flip-switch would do it (except you would have to flip it every time to use the carPC).