i would first try to make a hard reset: press and hold the menu and the select button untinl the ipod restarts - this will take around 6-10 seconds.
if the screen is still blank after resetting the device - i would open the ipod and check the lcd connector, maybe you should reseat it.
but wait until the ipod is in sleep mode and use the hold switch to prevent the ipod from waking up
if the lcd connection is reseated, i would check the funtion again, use the hold switch and wake up the ipod - if there is still nothing on the screen - it could be a dead lcd or the logicboard died