I have solved this problem with the help of telephone support. Initially I was disheartened after reading all that has been written in this particular article comments section, but luckily I managed to crack this.
I had earlier used a samsung with the mac mini, and straight out of the box, it matched with the samsung. It appears that this leaves the mac mini with the memory of the samsung. Hence when connecting with HDMI to a Sony Bravia, the mac mini did not recognise the Sony and vice versa.
I switched off the mac mini, disconnected the HDMI, connected it back, switched on the mac mini, AND HELD DOWN THE OPTION BUTTON THROUGHOUT, then pressed CMD+F1. That did the trick partially. Then i restarted the mac mini, as before. Everything now sings.
I also have a USB out to my DAC for music, which is the principal purpose of the mac mini. That has stayed undisturbed. But in the quicktime / ELMedia player etc. to play the movies in different formats, it is necessary to switch the output from built in speakers to an amplifier (painfully, every time) and then the sound comes from the amp-speaker combo and the picture from the TV.
The less elegant way to do all this is to have a Apple TV connected by ethernet or wifi to your router, and a mac mini to the same router, and then the Sony TV will accept anything your mac mini has, provided it is iTunes compatible.
If the apple TV is jailbriken, then you can use some other formats and a whole lot of other programs. There is plenty of literature around the how and why of apple Tv jailbreaking.
Hope this helps everyone.