It sounds like a faulty monitor, it could be that a needle or two in the plug is hindered though too, but doesn't sound like the likely case. At first I thought it may have been your video drive as well. Make sure your graphics drive is in OK condition and plugged in right as well.
Or it may be a problem with the monitor + your video drive not working properly TOGETHER. That's not usually a likely case though but still.
Otherwise it's likely to be a dead or faulty monitor. Did you say it was new? You might be able to call the manufacturer, return it, and get a new one hassle free.