VGA to HDMI connection for new monitor

I have a old Dell Latitude D531 with only Serial ports. I had a additional large TV/Monitor hooked up previously( ( it had serial port connection) worked fine Got new larger TV / Monitor with only A HDMI connection. got a Serial port to HDMI adapter cable ( Belkin) still can not get new monitor to get signal. Tried to up date the ATI video card with no success Any additional thoughts or tricks to get VGA to HDMI signal ???