My Cruze just wouldn’t start, acting as though the battery is dead. I replaced the battery 9 months ago.
Doesn’t mean the battery is not dead. The one you bought may have failed prematurely.
Especially if the alternator is going out and took the new battery with it. (I mean I wouldn’t necessarily suspect the alternator in a 4 year old vehicle with an unknown number of miles, but we’ve seen stranger things posted on here 
)