As others have said, the Genesis has only one battery - it's in the trunk area. There are "jumper cable hookup terminals" under the hood, covered by a plastic lid. That's what AAA uses. Those terminals are basically direct wires to the battery; they exist specifically for jumper cables.
Typical things that make a Genesis drain a battery in less than a week:
1: a bad door switch or trunk switch so one of the courtesy lights stays lit. Fold the back seat center
armrest down and open the ski pass-thru plastic door... verify the trunk is dark.
2: On Tech package cars, the entire NAV+Stereo system has three states: ON, OFF, and Standby. When you first shut off the engine, the system reverts to the Standby mode; this is somewhat like the "sleep" mode of a laptop computer. If the engine stays OFF and all doors remain closed for 20 minutes or so, the system goes to the full OFF state. Any door/hood/trunk switch that fails to say "door is closed" will keep the system in Standby mode which will drain the battery in a matter of days. On my 2009 Tech, there is a small blue light on the CD/DVD slot; it blinks a few times as the system goes from Standby to OFF. See if your car (if it's a Tech package version) blinks the light within 30 minutes of shutting the engine OFF.
3: There should be a rubber bumper on the side of the hood - driver side, about half way between the windshield and the front of the car. This bumper pushes on the switch visible in the black plastic stuff surrounding the engine. That's the hood open/closed switch for the alarm. If this bumper is missing, or is too short (there was a TSB about this for early model year Genesis cars thanks to this forum), the bumper fails to push on the switch far enough. The alarm system and the stereo system interpret this is as "a door is open... we'll probably be driving soon so don't ARM the alarm and keep the stereo in Standby mode so it boots faster." There are several posts on this site about this bumper including references to the TSB.
4: The clamps that hook to the battery posts are somewhat intolerant of many
aftermarket batteries. Basically they fail to grip the battery posts tight enough - replacement batteries seem to have slightly smaller in diameter posts and the clamps simply can't be tightened enough to grip them. This acts like a dead battery due to a bad connection. Some folks have experienced "total electrical failure" when trying to start the car - nothing works - but slamming the trunk lid or wiggling the battery wires cures the issue. A different battery, or inserting a thin shim of metal between the battery posts and the wiring clamps, fixes this issue.
5: There is a ground screw/bolt in the trunk area that may be loose or corroded. Scraping the paint under the bolt helps make a better connection to the bodywork. There are special washers, called "star washers, for electrical connections like this. Basically they are washers with many little tabs/ears on either the inside or outside; these ears are twisted. The washer ends up looking like a small propeller or turbine
wheel. The bent ears dig into the body sheet metal and to the ground lug of the wire making a really good connection. I would add this type of washer if your car does not have one.
6: if a key fob is near the interior, the car systems again think "we'll be driving soon" and stay in Standby mode. One person on this forum had an issue where the battery would die after a few days and he had only one fob... the dealer lost the second one. It turns out the second fob was sitting in the windshield wiper area - not easy to eyeball but the onboard computers could detect it.
7: there are failure modes of alternators that causes the alternator to discharge the battery when the engine is OFF. Basically, a fault in the voltage regulator or a shorted diode (diode = electronic device that lets electricity flow in one direction only, similar in concept to a "check valve" in fluid/hydraulic systems) will cause the alternator to act almost like a short circuit to the battery when the engine is OFF. Yet the alternator will still be able to charge the battery (albeit slower than normal) when the engine is running. Some auto parts stores, and most places that sell batteries, can do "on vehicle charging system tests." By looking at "ripple voltage" they can detect bad diodes. Many places will do this test for free as it only takes a few seconds to do. Such failures typically do NOT illuminate the dashboard charging system warning light by the way.
I expect a few weeks is about the maximum time a Genesis can sit parked and locked, with the NAV+stereo in full OFF mode. A friend of mine has been out of town for over a year now; I have been taking care of her Honda CRV. If I don't drive it once every two weeks, it too struggles to start. When your car has problems... do the interior lights work? Do the dash gauges and warning lights illuminate if you just push the START button twice (foot off the brake pedal)? If so, that indicates some battery energy exists and that the battery cables aren't totally disconnected. Try turning ON the headlights... if they illuminate and stay reasonably bright for 10 minutes, the battery is fine. If they dim noticeably during that 10 minutes then the battery is low on capacity. Or the wiring is horrible.
mike c.