without a bespoke hardware testing kit you won't be able to test the parts, changing a part out would work but then you wouldn't know what to change out. could be a few things, loose flex cable, dead backlight, broken inverter (if phones even have them), Broken motherboard.
The list goes on m8, if you can MHL out of the device and go back to stock then I would do that and send it off for repair.
If thats at all possible.
Phones: Moto 888 - Nokia 6110 - Nokia 3210 - Nokia 3310 - Nokia 8210 - Samsung e250 - Sony F305 - LG Viewty - G1 - HTC Hero - HTC Desire HD - HTC Sensation - Nokia Lumia 800 - HTC EVO 3D - Samsung i9300 - Asus Prime TF201 silver - HTC One - Galaxy Camera - Z1