A display is a display - there are no Windows only displays - so no CD or installation software is required. Obviously you have a 'dongle' that you plug into your computer and then plug the display into that dongle. From your description it sounds like the display isn't getting a signal from the computer and being environmentally friendly, seeing no signal the display goes to sleep to reduce its electrical pull.
Try this first: Shut down the computer and display. Unplug the dongle from the computer and the display and then re-attach the dongle to the display and plug it into the computer. (In other words, jiggle the cords!) Now turn on the display and then the computer. Recently, I've had issues with projectors and the only solution is to restart the computer with the projector already on. Perhaps this also affects some displays. If you still have no picture on the external display open System Preferences and select the Displays tab. Do you see two dialog boxes (one for the computer and one for the external display)? If not the computer doesn't know there's a display attached. Probably the dongle is bad in that case. If you do see two dialogs try changing the resolution on the dialog window that isn't the computer.