Your monitor does not have a serial port.  It uses a VGA port, which is the old, outdated standard for video.  After that came DVI, which was a white connector, a little larger, with pins and one flat connector.  Next came HDMI, which is still used.  The lastest is DisplayPort.  Each new standard came about to handle higher resolutions.

Decide which port you want to use, go to Amazon, and get an adapter cable.