Any fluctuations of voltage on the S0 buses far enough to go out of spec will trigger the unit to go down to a lower state, effectively restarting as far as the user's concerned.
The fluctuation in voltage on one of these key buses can be caused by many different things, not just capacitors. Often times, a trace on the circuit board will pop, for absolutely no reason other than its Apple. I'm rewiring a u7000 chip mount right now on a 2012 MBP, that came in for a symptom of turned it on and nothing happened.
Although they didn't mention liquid damage, there are three spots on the motherboard, all on the underside, that caus ed the short that blew out the pins on the power and charge control chip mentioned above. Three traces were blown out from under the chip completely, making simple chip replacement not possible even if the chip was bad.
I'm using extremely fine magnet wire to make the connections on the motherboard that were blown out, one of them being a via.
In addition, on this A1398 The users left side toward the hinge is where both the mag safe and the LCD connectors are. As another user said, the LCD backlight driver, which is bumped up to 45 to 47 volts, is common to blow as a symptom, but once they go, they go. There is a fuse that can blow in addition to the buck up converter chip itself.
These are common things to go bad in that area, especially traces coming right off that mag safe connector. Another thing to consider is that where you saw the smoke might not be where it came from, but just the place where the smoke was able to escape.
The first thing I would check is to see if you can run the unit on battery as well as AC/magsafe. That tells you right there if you have stable s0 and your power management chip is functioning properly. That chip is the one that decides whether or not you have the correct charger plugged in and the right voltage for it to allow charging of the battery. It also checks to see if the battery is operational with the onboard chip in the battery pack as well as the voltage coming off the battery (batteries).
Apple doesn't actually do any repairs, but they use as a place to solve user problems AASPs just like mentioned earlier at places such as Best Buy. Please Google for videos about them before you decide to roll those dice. Apples inability to help their customers, and their fight against right to repair (#RTR) are the reason I got into fixing their laptops in the first place.
I think you should find a repair shop in your area, weather certified by Apple or not, and go by the reviews. try to find objective reviews on sites other than the vendors site. When you drop off the unit for repair, be sure to enter into a signed agreement that you should read carefully that covers you for items that they damage in the course of repairs, and getting any repairs with costs approved by you in advance.
There are a ton of really great people fixing Apple products for all the right reasons, and there are disreputable ones that are doing it for all the wrong reasons. Just be careful to make sure you're using a place that is reputable.
If you don't find a place locally, there are fantastic shops that will take your unit via mail, and you will more than make up for the shipping in quality of repair. I'm probably not allowed to mention any of them, and I don't take mail-ins, but it won't take you very long if you search to find out who the really good ones are. Look for the ones that have hundreds and hundreds of YouTube videos showing how they repair their units. those are the kind of people you want to associate with, not the ones that are so bad that they don't dare video what they do.
I'm sure someone will eventually say to run apples internal diagnostics, which are essentially useless, and there are other hardware tests out there, but You really need to have someone get their hands in there and see what's really going on. You might be seeing a symptom of something that started a long time ago, like the three areas of water damage on the 2012 logic board I'm working on right now.
The pain of poor quality lasts far longer than the joy of a low price.
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