This is likely a High-bandwidth Digital Content Protection (HDCP) issue. If you are converting a video signal from a device that can play copyright-protected content, HDCP will block the conversion to an analog signal (for example, VGA) or to any video capture cards.
You will likely run into this issue when you use devices like Blu-ray players, DVD players, and certain gaming consoles. For more information on HDCP and gaming consoles, refer to the following FAQ: https://www.startech.com/faq/video_capture_cards_video_game_console_compatibility.
Some video cards also output an HDCP signal full time. In this case there should be an option for your video card to disable this feature. You might need to contact the manufacturer of your video card for more information.
Adhering to HDCP is required for converting all digital signals to analog signals or to video capture cards. Unfortunately, there is nothing you can do in these situations other than convert to a digital display.