[PTTG]

Cold reduces the reaction rate of a battery, but not significantly compared to just sitting out in the elements. If you want the PCs to be able to find a few charged batteries when all the other ones are long dead, go with supertech, or at least supercapacitors. There's not a significant enough difference between normal battery chemistries to even exaggerate in a cinematic game.

Electronics in general, if they were protected from the initial EMP or whatever caused the apocalypse, could survive for years provided a dry and reasonably temperate environment. Realistically, they would need cleaning and stable power to use safely, but cinematically, you could get away with just plugging it into a dusted-off solar panel or electricity-themed super.

Solar cells decay over time (the oldest ones around still function at like 60% their nominal capacity), but if they aren't cracked, they will still work for a looong time. Decades, though the inverters and storage systems they're hooked up to will fail much sooner.

Gasoline goes bad within 3 months worst case, but even non-cinematically, a well-sealed and well-blended mix might last for at least a year or two. Cinematically, the gas is always good, even if it's moonshine.

You might rely on cinematic forces to make some post-apocalyptic hazards more severe. Cinematic nuclear fallout -- even in the case of non-nuclear apocalypses, plants and storage areas fail -- becomes an immediately deadly threat, rather than a statistical one involving decades of increased cancer risk.