Why won't my iPad turn on?

Has the iPad ever been worked on before?

Has it recently suffered any falls or water damage?

Unless they disassembled it at the apple store and tested the battery, they wouldn't know whether it's the battery or something else. The first step on this repair would be to clean the charge port very well, then try charging it. Try a new cord and power brick if that doesn't work. Also see if iTunes recognizes it, the device could be in DFU mode. If those fail, then you will need to open the iPad and test the battery with a multimeter. You will want to ensure that it is producing the voltage written on the battery, or slightly more. Also ensure the charge port is plugged in. I'm sure you will find your issue by this point, I've never seen an iPad board just go bad out of the blue like that.