A common reason for this behaviour is a flat battery. The solution is to connect the charger and wait. For my DR1000 it's usually about five minutes till it starts to show life signs, but I've heard people speak of hours too, or leaving it overnight just to sure.
Given that you have a brand new battery that the device still needs to get used to, it may take a while (and it's also best to fully charge it, which takes a couple of hours usually). If it does not spring to life, either the battery or the device is probably broken.