So... pull the code and see what it's whining about? If the MIL is lit, there will be at least one stored code you can pull, or a local parts store can pull or... seriously, just go ask the car what it thinks is wrong instead of speculating. It could be totally and completely unrelated.
If you own a modern car, you should own an OBD-II reader. And a voltmeter. They make life so much easier it's not even funny. I don't have to guess that the idle issues are a sticky idle air control valve, the computer is shouting, "Hey, my idle air control valve isn't responding right!" if you go listen properly. Or a weird roughness under load, hey, misfire on cylinder 3. Yup, plugs are ancient. Etc.
The little jump start lithium packs are nice enough, I hear, though I've not found any that can do 6V as well, and about half the time I need to jump start something, it's a 6V system.