Check Engine Light after jump start

try disconnecting the 12v negative for a few minutes. also, what voltage is the 12v now measuring? you may have seriously compromised it.

 

Just have the dealer to take a look.

 

Personally, I would ignore the CEL (as long as everything seems OK) for a couple of days and see if it resets itself. Just what I would do, but what do I know?

 

I've seen cascading failures as a car's battery dies. It usually results in network failures as various modules (the ones sufficiently downstream so that the added resistance on the power lines drop them out first) begin to fail from power loss. These usually result in the CEL lighting off. I've seen some cars clear them automatically but sometimes you need to do it manually.

 

Assess the 12 volt battery, or get it assessed. The most rudimentary approach, just see what voltage it's reading, when the car's off, after sitting overnight. Better: do an electronic load-test, with something like the Solar BA5 (or BA7), or get an automotive battery retailer to do it, they typically would have a pro-level tester of that sort. Or the dealership could do similar, but they'll likely charge you (no pun intended), somewhere between $50 and $100. Or they might do it for free.

You've likely partially run down the battery, due to prolonged use. It's not a big battery; you pretty much have to avoid this kind of use, completely. A jump start does not restore it completely. A full session with an appropriate smart charger probably will revive it, but it will be somewhat compromised, I would start shopping replacements sooner than later, say 4 years vs 5.