There's no way to start an engine without stored energy of some kind. The only way that's reasonable that doesn't require stored energy outside your body (you're still using stored energy in the glycogen and ATP in your muscles, and in turn blood glucose and stored fat and protien reserves...) is to use something like a small alternator on a weed eater or small briggs engine, forming an APU, and perhaps a small battery or ultracapacitor, preferably the latter, since they have shelf lives in the vicinity of several human lifetimes, so that you can charge said cap up with the APU, then use it as your starter battery. The cap has the advantage of being able to store up charge at a rapid rate, and release it even faster, and since you only need to get through one or two revolutions for the motor to start, generally, you don't need a whole charged battery to do it, just something capable of dumping enough amps to run the starter motor for a second or two. The advantage here is that you're pull starting the briggs or zenoah (they make most of your two stroke weed eater motors in the U.S.) and it's also a handy little APU for other things like charging battery banks at your BOL and the like.
The only other option is the cartridge start method, whereby you stock up on 12 ga blanks and git-er-dun that way. Still stored energy, but if you can't unload buckshot and just use the powder charge post SHTF, then you've got other things to worry about than not being able to start the car - you need to find yourself some buckshot, and a knife, for a variety of other purposes.
The CO2 thing is a viable solution since you'd have one or two of the tanks under your seat,and they'd only be used as a backup until you got your battery fixed, but the disadvantage of anything other than the APU setup is that it will only work on your vehicle, which you have modified for the backup solution in advance. The APU doesn't have to be permanently mounted anywhere, and if you use something like a motorcycle alternator and the weed eater engine, then you should be able to put it into a box about the size of a loaf of bread - and I'm willing to bet it'd weigh less than 15 pounds if you use a stock polyethylene gas tank for the weed eater. Just be sure you store a bottle of 2 cycle oil with it, or go with a 4 stroke weed eater.
