firstly I'm going to admit to not having read all of this thread...
so some points i raise might have been said before...
#1, no don't put batteries back to back, there is a very good reason for this...
I see your logic here, 12v + 12v = 24v, or, the way that you'll arrange then -12v 0v +12v
however, the complete car chage circuit only delivers about 14 volts from the alternator, so you'll never be able to charge the batteries, also your earth would essentially drop to -12v if you tried, so you'll likely fry aother things in the vehicle.
assuming that you were trying to connect the batteries in parallel not in series, then yes, this can work, and this is something that people with high power sound systems have been doing for ages, however you'll still be stuck with 0-12 volts, that are not good enough for a computer that needs negative voltages as well as positive.
in any case, after the batteries start charging the voltage isn't quite as regulated as you might like, the alternator will provide ~14 volts to charge the battery and power all electronics/lights. and there will be voltage spikes in that as well.
in order to supply an off the shelf computer you're going to need an inverter, and it's going to need to be a fairly beefy one to power a computer, depending on what you have in there.
of course you can use lower spec components, by that I mean a low powerd PC, (assumng you're not trying to fit a high end gaming rig in the car). low power PSU, something with integrated video and sound.
also if you used laptop hdd drives they are lower powered than standard drives.
(and there is even the possibility that you could use compact flash to boot from to a cut down linux build and have and media on USB flash drives or something).
You can buy off the shelf carputers, that will fit under the seat, or you could always make a case to go under the seat. or indeed some people create car puters that fit inside the spare wheel in the boot as they take up no additional space and are hidden under the boot carpeting as well.
if you wanted to go really low power, but also really cool, then i'd have to recomend either something from a company called ARCOM (who make small form factor mainboards) available from RS in the UK
ideally I think that in that case you'll be looking at something like an early pentium or something that doesn't require a fan on the heatsink, in this case however I suggest putting a fan on the heatsink to help circulate air around a place that's now going to have very restricted airflow.
or just go the whole way and use an old PDA, -that's what i'm planning to do in my car.
the PDA has everything you'll want in it
(for instance the one I'll use has gp built into it, a card reader, (sd card slots can be used to plug in an SD wireless card for syncing things).
there is also a full colour mini touch screen, and battery, (so if you stall there isn't a power interruption as you turn the engine back on).
(this is what happens with my current in car juke box that uses a regular 3.5" HDD, as it draws some 4A to run, so when turning the engine there is just not the available amps, so the system crashes and needs to be restarted.
(would not be as easy with a full PC which could become corrupted over time).
