First thing to do is power off, unplug system and disconnect and reconnect the LVDS cable that runs between the mainboard and back of the display panel.  Check the cable for evident damage to the wiring and connectors - if it's damaged, replace it. 

If that does nothing, replace the display panel.

Service manual:

http://www.dell.com/support/home/us/en/19/product-support/product/studio-1558/manuals