iPhone 5 shows red empty battery with charger plug but doesn't charge
I broke the screen on my iPhone 5 and replaced the screen, as I have successfully done before. When I plugged it in (it had run out of power just before the screen broke) I see the graphic showing an empty battery (red on one end) and a charger plug being inserted, which is what I've seen when it's charging but doesn't have enough charge yet to start up. But, even after leaving it charging for a while, that image never changes so it seems like it's not charging at all.
I'm not sure what to do. I may try to get a new battery but it seems strange that the existing battery would just die like that so I'm thinking maybe the impact had loosened something but all the connections seem ok.
Any idea what I should look at?