Laptop shutting off without AC Power, Battery seems fine?

[PantheraAter]

I have a Lenovo Y-50-70, for a while I've had an inflated battery that I didn't notice. The battery was inflating over several months and I just had it removed and replaced with a new one.
Right before I replaced it, the laptop began shutting off along with the regular power outages frequent in this country, and I took it down to the shop to get it fixed and they swapped out the battery. Before that, I used some diagnostic tools to check the health of the battery and it said it was fine.
Today, after leaving my new battery unplugged for a while to drain, the laptop shut off again when not connected to the AC power. I am currently looking at the battery meter and it says it is charging, the computer shop doesn't open again until Monday and I'd like any kind of advice that I can offer them for when I bring it down.

 

[webworkings]

If they used a cheaper battery (not OEM) it is possible it is a faulty battery. There is really nothing you can do about that until you get them to give you one that is working properly.