Won't turn on with battery in after it been sitting a while

First off the model is dv6-7210us, but that was not one of my choices on here.

I have a weird scenario. I bought a new battery for this laptop. When you first plug in the battery and press power it works fine. The battery reads and charges. However, if you leave it sit shut off for like an hour or more then press power nothing happens. It doesn't matter if the power cord is plugged in or not. I have to pull the battery out and either plug it back in or just run it off the power cord to turn it on. Can't seem to figure this out. This is something I am donating to a learning facility for kids with reading problems. I need this to work right.