Troubleshooting a 24-inch Asus LCD display that is flickering can take you down a number of different roads, but each troubleshooting test is relatively simple. Flickering can refer to a number of different interruptions in the video display, some of which can mean serious trouble with the actual display hardware.
Reconnect video signal cables both on the monitor end and the computer end. Also check the cable for any breaks or kinks that could be interrupting the video signal reaching the monitor.
Check to be sure that there are not any devices that may be causing electrical or radio frequency interference near the monitor. Interference of this nature can cause something called "hum bars" which are horizontal distortions that run up and down the monitor. These can usually be eliminated by plugging the monitor into a surge protector or battery backup.
Force an update of the monitor's Windows driver by entering the Device Manager through the System control panel. Under the monitor heading, you should see a "PnP Monitor" item. Right click on that and select "Update Driver." Click "Next" until you hit the end of the update wizard. Updating the driver can offer more resolution options in the Display Settings, letting you set the display to the optimal resolution.
Go into the Windows display settings and make sure the resolution is set to the optimal settings for the monitor. For an ASUS 24-inch monitor this is 1920 by 1200, and requires a 60Hz refresh rate. Adjust these settings in the advanced adapter settings in Windows, under the Monitor tab.
Have another monitor handy to test, just in case the flickering is a problem with the video card.