It is a frame fault but Sony TV's of that age suffer from lots of dry soldered joints and leaky electrolytic capacitors and they're usually not limited to just the frame circuit. At that age I'd be checking all over each circuit. Pushing the on/off button repeatedly could cause bigger problems.
You could still ask for an estimate.
As an educated guess; it'll probably cost you £40 - £70 if it's just soldering, depending on how thorough the engineer is (ie. time) and approaching £100 if it requires capacitors and frame IC as well as the soldering. Unfortunately, your TV will still be old at the end of it.
Be prepared to buy new but take it to a reputable dealer and as long as you don't waste their time they may be prepared to take a quick look at it free before you commit to buying a new set off them. All we dislike are customers who ask us to take a quick look at their set and if advised it's not woth repairing, they go and buy elsewhere. You might be lucky and they'll fix it for much less than a new TV.
Cobweb
July 2006