Connecting Galaxy S3 to DisplayPort via MHL HDTV Adaptor
A few things to consider:


Make sure the HDTV adapter is connected to a USB power such as the wall or a PC (the USB from the TVs don't give enough power)
Have you tried the HDMI to display port adapter with another HDMI output such as your laptop or PC? maybe this is faulty
Try using an HDMI to DVI adaptor
Try another HDMI monitor to ensure its not your monitor