I have a 2013 Air I use as my main machine. It's hooked up to a 24" LG IPS monitor via a thunderbolt HDMI adapter. So the adapter plugged into the Air then HDMI from that directly into the screen. I want to leave the Air's lid shut all the time and use it as a desktop. The problem is when I go to use the computer and turn the LG monitor on sometimes theres nothing on the screen. It's just black. I open the lid of the Air and that screen is blacked out as well. I've tried plugging and unplugging but nothing works except turing the Air off then back on. It seems like it has something to do with the HDMI handshake between the Air and the LG monitor. The HDMI adapter is made from RocketFish and I also have one from eBay which behaves the same. Does anyone know whats going on? Would a straight Thunderbolt HDMI cable possibly fix this? Or what about an Apple brand MiniDisplay Port to DVI then DVI into the monitor? I'm lost on what to do and it's driving me crazy as this is my only machine for the moment. Any help is appreciated! 
