Either the genius is correct and it's the motherboard, typically referred to by Apple as the logic board, or it's just a dead battery. The clock reset suggests a dead cmos battery. Here's an
ifixit link that mentions that part. This would require a new logic board. You might see if depot service is offered here for out of warranty repair. Did you purchase this used? You mention not knowing which one. You have to know exactly what macbook pro or macbook you own to know if any do it yourself repair options are available. Without that information anything anyone can link is useless. It's also possible that the dead cmos battery killed off your main battery if the Mac relied on it to keep time after that point. I'm not sure if it works that way, but if it isn't charging, it's possible.
Their standard recommendations can be quite expensive out of warranty, and some of them are far from being geniuses. The OP really needs to take his info from about this mac and reference it with something like everymac or mactracker to ensure he provides the right model. Beyond that asking the genius for further detail may have been a good idea.