Since a 2016 model is at least four years old (nearing five years) it is unlikely you still have a warranty on the laptop. Unless the laptop qualifies for one of the free Apple repair programs, then any repair costs are the responsibility of the owner. Only Apple can confirm whether the laptop is covered by any warranty or free repair programs since Apple does not list all of the qualifications online (in fact many times even their own techs have no idea since Apple bases coverage solely on the system serial number in many cases). If the Logic Board has been identified as the culprit, then I'm not aware of any free repair programs for the Logic Board.
https://support.apple.com/service-programs
There are a lot of ways a USB-C Mac can fail. A third party charger or peripheral can easily damage a USB-C port which can then prevent the Mac from receiving power or charging. In fact in some cases if the chip protecting one of the USB-C ports is damaged it can prevent all the other USB-C ports on the laptop from charging or powering on the laptop even though they each have their own protective chip. Plus sometimes electronic components just fail.
Without seeing the laptop first hand there is no way anyone here can provide any specific reasons for the failure of the Logic Board. The tech working on the laptop would be in the best position to tell you, but many times they have no real technical knowledge since Apple doesn't provide any real substantial technical repair information to anyone. If you want that kind of information, then you would need to find an independent third party repair shop that performs board level repairs to assess the issue at a lower component level, but finding a reputable and knowledgeable shop/tech is extremely difficult. Even then, they may not always be able to tell you what caused the problem. Plus Apple will most likely refuse to repair your laptop in the future if you use a non-authorized shop to repair the Logic Board.