Would really just need to power a water pump get running water going for farming. I'm sure there would be no car battery shortage find some solar panels later for lighting and non essentials later.
There may not be a shortage of car batteries, but after 2-4 weeks (sometimes up to 8 weeks) of not being used, the charge drops pretty low. However, a brand-new, disconnected battery can last up to about six months. I think the early weeks/months would be the hardest because it'd be total chaos. Also, there would be a ton of zombies probably running around, so trying to snag a car battery may be a pain, especially when there's no way to know if it's even any good.
As far as the solar panels go, I think that'd be a great idea, but the logistics of actually getting solar panels may be a hassle.