I can either have the media player on the computer screen or I can drag it over to the projector screen
This suggests that you are using a desktop rather than a laptop - correct?
With a laptop the Fn key plus the display key toggles the display between laptop, secondary display or both.
A desktop is a little different - I guess you have 'Extend my Windows desktop onto this monitor' set in Windows display properties (Control Panel > Display)
Look in Control Panel for an icon relating to the graphics card - on my box for example it is NVIDIA Control Panel as I have an nVidia card. There may also be an icon in the Notification Area by the clock.
The option you are looking for in those display properties under dual/multiple monitors is 'Clone' which puts the same display on each monitor.