Usually there's a trace on the board of TV tuners that's made to blow before it shorts anything. Maybe a center piece of coax broke inside the F connector and fell in, shorting the connector, or something in the tuner may have shorted. Is the F connector loose, or the center hole all widened out and messed up? A bad F connector could cause that.
If you're good with soldering, you could replace the tuner, but it'd be best to check the voltages on the pins and all 1st and make sure it is the tuner, I don't have a schematic for Bravia's, so can't tell you what they should be other than one will be 5v and ground. There will be a label on the tuner with a part # on it if you open it up, I may actually have a used tuner here if you do need one. Some Tv's have an isolation block before the tuner, it'll be a small box that the F connector is a part of, and a coax wire from it connects to the actually tuner, I have seen the caps in these short before. Any one of them should work to replace that, as long as it physically fits.
What is the model# of your Bravia and what does it do when you have the coax hooked up to it with a known good signal?
