Will VGA cable work on TV's RGB port?

The HDMI connection between my Mini (late 2011 model) and my HDTV has malfunctioned and resulted in a "no signal" on the TV screen. I tried 4 other HDMI cables and got the same result. I'm deducing that the issue is the HDMI port on either the TV or Mini.

I'm going to buy a Thunderbolt to HDMI cable (in case the issue is the Mini's HDMI port). I'd also like to get a HDMI to VGA cable (in case the issue is the TV's HDMI port).

However, my TV has what I call a VGA port labelled as RGB (D-SUB). Will a VGA cable work on this port?

Also, if I'm using the TV's VGA port, is there any quality difference between using HDMI or Thunderbolt on the Mini?

Thanks in advance.