1. Press the Power Button.
2. You will see the ASUS logo for about 5 seconds.
3. The "VGA no signal" message appears.
4. Depending what ASUS monitor model you have, there should be a button on the bottom of your monitor that looks like a rectangle (representing the monitor) with an horizontal line from left to center. Press it as soon as you see the "VGA No signal" message. The button icon might look like this:
5. Doing so will now switch to "No DVI SIGNAL" message. If you are using a DVI cord, after a few seconds the Desktop will pop onscreen. If you are using a HDMI cable, however, you must press the Mode button (#4 above) again until it says "HDMI" onscreen. After a few seconds, the Desktop will pop onscreen.
NOTE: Clicking that button many times in a row will not do much. You need to physically see onscreen when it switches from NO VGA SIGNAL --> to NO DVI SIGNAL --> to HDMI. Wait a few seconds between pushing that button until you can read onscreen the messages. Once it sits on HDMI, wait a few seconds until the Desktop shows up onscreen. Same if you are using a DVI cord.
I had this same problem just now. I loaded this page to find a solution. I couldn't find one, so I troubleshooted on my own and this is what made it work. My model is ASUS VG278HV (27").