Sounds like a tuner related problem. I have repaired several Sony's (amongst others!) with bad solder joints on the tuner.
My fix has been to de-solder the tuner from the mainboard, then remove the shields and inspect for cracked solder joints. This issue has been quite common on tube-type TV's from the 90's; poor soldering quality from the tuner vendors.
If you have electronic experience, this is a simple fix, but not for novices - televisions can maintain a lethal charge in the tube even when unplugged.
Feel free to contact me through electricalrepairlinks.com if you need any additional information.
Tim, January 2007