I've had a couple of laptops that turn off automatically, but I haven't yet seen a laptop that turns on automatically.
If you search the forum, you'll find a $30ish module sold by another member that will do that for you, but you'll have to solder it to your laptop's power button, which may be hard or easy depending on the laptop.
My installation involves a laptop using the w3bm4st3r's auto-on module (self-made, it's about $20 to DIY with RadioShack parts), which you can find here
But as to hibernating when you switch to battery, yes, there's something on this site for exactly that purpose, called ShutControl. Between the two of those, my laptop powers on when I turn the key and hibernates a few seconds after I remove it. Yay!
Why not just use standby, no hibernation. Now all you need to do is tap the screen or hit a key and you will resume in seconds. Modern laptops use very little power on standby. My laptop can last over a week in standby. My car does not stay turned off for more than a few days, and when the car is on the battery is getting charged again. If your accessory outlet stays on when the car is off I would still expect your car could keep the laptop charged for a few days without ending up with a dead car battery, use dc to dc to save power, or rewire the accessory outlet. I used to have a BMW and the radar would stay on when the car was off but it never made a difference, but then again it had a massive battery in the trunk.
I don't own a Carnetix, but I believe the P2140, at least, has a USB interface and software that can tell your machine to execute power management commands when ACC power is cut, and I believe has some ability to send a wake command via USB or momentary relay.
My laptop knows when it switches to battery power, though, so using ShutControl I can power it off (with a software-adjustable delay) when ACC is cut.
Assuming you want to hibernate/power down, something that trips the momentary power switch might be your only option, though I have known some machines that will wake from hibernation on LAN (not my laptop).
If you go that route, you can survive with a much cheaper power supply:
That model is discontinued, so it's being sold for a very low price. My laptop takes 19V/3.4A (like what the Carnetix would supply) and fits a "Size N" (according to RadioShack) DC plug, which works fine with tip #4 on that adaptor.
Upshot? It's just a power brick and puts out very little heat with no fan! Nowhere near the intelligence of the carnetix, but hey, it's like 1/5 the price.