Check the owners manual and the rear of the panel for any inset reset buttons. In particular if its a Sharp rebadge - I own two older Sharps that have a power setup systems that requires a reset so that during power outage issues this can occur (but sound always remains with no picture) and I have to insert a thin device into that inset button and leave it off for about five minutes and then reboot fresh and they are back to normal.
However, I don't know that this is an issue on newer Sharps built today since I don't ever recall ever seeing anyone post about this PITA event on current models.
Just a possible thought that may be on yours since half of Sharp's production globally gets rebadged by others - check the owners manual or back of the set for any power protection resets. Good Luck!
I've also had a similar event as yours on a particular cheaper LCD monitor lines on my network and my Tech Assistant and I decided to disassemble a few of the failures layer by layer since they were beyond warranty after viewing the EngineerGuy video of how the Monitors are assembled and work and we found on this cheap line that the thin backlit tubes at the top/bottom the connector ends top or bottom would literally burn out - very cheap power components/connectors - I won't be buying that line again anytime soon for my network -Brand was AOC .
For an interesting EngineerGuy demo view here: (The Forum should have a sticky area and post Demo's like this - extremely interesting)http://www.engineerguy.com/videos/video-lcd.htm