The problem is that VGA is analog and HDMI is digital. There is no adapter for VGA to HDMI because the HDMI port will not accept an analog signal. Well actually there are HDMI to VGA cables, but they are for send video from HDMI to VGA, not the other way around.
You will need to buy a VGA to HDMI converter that basically converts an analog signal to a digital signal. Here's an example of a VGA + Audio to HDMI converter:
if your tv doesnt have a vga connector then surely it must have a dvi and they do make hdmi-dvi adapters. I'm surprised one didnt come with your GPU. You will still likely need to run a seperate sound cable to the tv.