Monitor won't work with Minecraft?

I have tested this by plugging in my monitor to attempt to play minecraft, but it said the graphic drivers were bad. One day I decided to do it with the HDMI and it worked! When I plugged the HDMI out and plugged the computer with the monitor again, I was able to play minecraft. Is there any easier way to do this? Is this really the monitors fault?

With no clues on anything about "monitor" or "graphic drivers" on some video system in some "computer", how to guess?