Nothing displays on screen at all? I guess before we really get into it has there been any damage to the device? A drop, a brief swim, sat in an overheated car or near a heat source for an extended amount of time?
How did you first notice this issue? You woke up to it not responding to attempts to turn on the display, you were holding it and the display went out, you were using it and at commercial break went to pick it up and no display?
So what happens when you plug it in? Does it display a percentage of battery or any indication that the device is charging?
What have you tried? Holding the power button for up to 1 minute, trying to boot into recovery or the bootloader by holding the vol down button and the power button, (I'm not familiar with this exact device it could be hold the power button and vol up, or it could be hold the power button vol up or down and the home button), anything other than just pressing the power button?
Does this device have a removeable battery? Have you pulled the battery for 1 minute to 90 seconds then put it back and attempted to turn the device on?
Have you tried removing the SIM card and powering on the device?
I'm assuming along with no display there are no sounds coming from the device? So pressing the power button for the length of a normal power up and waiting long enough for the boot sequence to complete, maybe seeing those lights turn on or even flash, and trying to call the device from another phone just to see if it rings. This could help us know if the phone works and only the display is malfunctioning or if the device its self is malfunctioning.
Have you plugged it into a PC or laptop to see if the PC or laptop recognize the device? Again this would be an indicator of the device working because they won't recognize a powered off device, usually.
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