Why won't my camera turn on?

I just got a second hand camera from a shop- the piece supposedly worked fine but was used to showcase it at the store, and because of that the charger was missing, so when they were selling it I got it for a pretty penny.

I had to use a different charger, which Barely seems to be working, and I have NO idea if the camera doesn't work, if it's the battery, or if the charger is ruining my life.

I'm a photography student on my first semester and need to use this for an assignment within a few days. Please help.. I just need to try something and anything to see what's wrong