Folks - I finally made it work! Here's the update to my problem and what I went through to connect my HTPC to the Projector through HDMI.
The first problem I encountered when I tried to connect my HTPC to the AV receiver through HDMI, there was no display. Upon reading the fineprint of Onkyo's manual, I found that a HDMI input cannot be down converted into component output and therefore, HDMI input can only be passed out through another HDMI out! So, my entire HTPC failed as my Onkyo is connected to the projector through component cables.
The second issue was that, as with most Indian homes, pre-wiring is done using 3/4" or 1" conduits which is too small for the HDMI connector to fit in. So, that ruled out direct HDMI connectivity. Also, because my projector is ceiling mounted, I have to go through atleast three 90 degree bends which may not be supported by the HDMI cable.
I tried to buy some locally made cables which purported to convert HDMI into component. I learnt the hard way that such a thing was not possible as HDMI is all digital while component is analogue.
Finally, after a great deal of research, I decided to go for a HDMI balun - a converter which can use CAT5e LAN cable instead of HDMI cable to carry the digital data. I enquired with local sources and found them too expensive (around Rs.10,000). So I decided to order them online and selected the least expensive balun - Sabrent HDMI CAT5e balun. I also bought some HDMI cables from the neighbourhood electronics shop (nothing high end).
They finally arrived and I immediately called a networking technician to do the LAN cabling. It turned out to be a successful setup! My projector was displaying Windows and all seemed fine. However, when I tried to play a movie, my Onkyo kept displaying "No Signal" and I could not hear any audio. After tinkering and googling turned up nothing, I tried changing the desktop resolution from 800 x 600 to 1280 x 720 (720p). And lo behold - there was sound! There's something in the Onkyo specs which recognises HDMI audio only if the video resolution is atleast 720p!
Then I discovered that the picture was not filling up the screen in the same way my DVD player did. Changing the resolution did not change the display size and I had black bars on all sides of the screen. After more googling, I realized that ATI had a small feature called over/under scan in its control panel and that I need to reduce the overscan to zero in order to fill up the projection screen. Finally that worked.
Then, I realized that the sound I was getting was not true bitstreamed audio. Which meant that my Onkyo display would show "MultiCh PCM" and I would get multi channel sound, but my sound card (ATI HD5850) was doing the audio processing. After more googling, I realised that VLC media player does not support bitstreaming (pls correct me if I am wrong). WHen I used MPC-HC player, the DTS and DD icons on my Onkyo would light up. Same case with Windows Player. So that issue got resolved.
Finally this is my setup:
HTPC (HDMI) -> Onkyo -> HDMI sender Balun => CAT5e => HDMI receiver Balun -> InFocus (HDMI).
I have written this down so that it may be helpful to someone else who is also going through the same issues as I am (and there are lots of them, according to Google!) While I am relieved that I have a superb and inexpensive working solution, I hope that this will also work with a Full HD projector (future upgrade!) with 1080p video and TrueHD audio. Because if it doesn't, I'll have to start tearing down some walls and start laying new conduits!