This is a known bug with some versions of Evo 3D. When the battery is completely discharged, the phone will no longer recognize the battery & charge it despite it being put on charger. Some say it also happens when CWM recovery is installed which does not charge the battery when the phone is shut off. Apparently this looks like a display problem but it's not and phone does not start because battery has no juice left.
Try the following methods one by one to let the phone charge the battery again. Any of this methods has worked for many.
Pull out battery, press the power button for 15 second with battery out, put battery back in phone. Let it charge and then try to turn on.
Pull out battery and put back in, set switch for 3D to 2D, plug in power cable, hold camera button and then power button.
For this method, you'll need HTC drivers installed on PC, Android SDK OR adb command executable. Remove battery & put it back in. Connect phone with PC. Open Command Prompt window, go to ADB folder & type adb reboot-bootloader. Phone should charge, let it do that for half an hour and restart.
If you have external charger, try charging the battery in that.
PS: Faced the same issue earlier & tried all the above methods. None worked & finally issue was resolved after replacing the battery but i was on earlier version of firmware then.