Why do BOTH of my LCD screens flash on briefly?

My daughter's DSi slid off the coffee table in the living room and hit the wood floor. Now when the Power Button is depressed, both LCD screens flash on for a second, but then the machine shuts down. I am a homemaker and mother of 2 young children who love their DSi consoles. I am hoping that this problem can be solved with little or no cost to me, as these units are not cheap to begin with. The charger seems to work fine, as when it is connected and plugged in, the orange light remains constant. I also checked the battery and connections. They seem undamaged, and worked fine in my other daughter's console that did not hit the floor! I am somewhat technically savvy, in that I can program my DVD recorder and work my smartphone, so hopefully the fix won't be too complex! I have never opened up the DSi before, nor do I own a "spudger" tool. Please help if you can. Thanks!