My Dear Friend,
FYKI when HDMI cable is attached to set top box it's all component port will not work this is the way STB works, only S/PDIF (Coaxial Port for High End Audio) works. Thanks for your concern and I’d like to say that I implemented all the options already.
However I found the solutions which will definitely the cheaper way to watch
TV in HD mode with your own HD STB (Except Videocon D2H HD STB)
1.) Use this Converter
http://www.ebay.in/itm/HDMI-to-VGA-Converter-Adapter-Cable-with-Audio-Plug-n-Play-/261468401122?pt=LH_DefaultDomain_203&hash=item3ce0bb2de2&_uhb=1. Quality will little reduced but believe me output will be around 1080 if your STB is having HD Channels allowed.
2.) Connect your HD Monitor with HDMI cable directly without any converter and use the S/PDIF/Coaxial output of your STB (reason I already told you above), and connect with a connector readily and cheaply available in the market.
-Mayank