Android phone won't turn on go to recovery or charge

Ok so we bought a Plum z516 for my son for school a few months ago. He started having a problem, where the battery drains fast and he has to charge it. A few times it refused to charge but eventually started charging after he just left it alone connected. He came home last week saying that the battery dropped to 0 fast and the phone shut off. We put it to charge but it only flashes the plum logo every 10 seconds. It does the same thing with a different charger. Plugged it in to the pc, it is not recognising it. Tried to boot it in recovery mode, not happening either. I tried the freezer thing, did not work. pulled apart battery and sd card, sim card, did all sorts of shenanigans I found on youtube too. What is causing this? Is there a fix? We have no money for a new phone and I have no idea the cost to repair