i) Does your Bravia have a PC-in ? Many LCD tvs are effectively monitors also.
ii) You might need a "TV Out" - some graphics cards (I thought most) these days have them
iii) If your Vaio outputs DVI and your Bravia has HDMI input (I suspect it will have) then you should be able to use DVI to HDMI.
Also worth asking on click here if you don't get a response here.