The fault is one of the most common failures TV engineers see and usually straightforward for an engineer to repair. Often, these repairs can be carried out in the customers home.
On a TV of this age, it's likely that the frame output I.C. became dry jointed (poor solder on its connections) and failed. Possibly some electrolytic capacitors in the same circuit may need replacing too, as they too tend to break down as the TV ages.
Neither of these components is or should be very expensive.
Typical costing..IC maybe £8 - £15, Capacitors maybe a couple required at £1 - £2 each. Plus Labour charge say £40 - £70.
There is a good chance that the frame output IC for your TV is available after 11 years, although I will warn you that there are a few frame IC's (eg. the TDA8175), used in some Panasonic models, around that era which are discontinued.
If you enjoy this set and the picture was good before failure, it's worth repairing, although you might ask the service agent, to supply their estimate first.
(PS. Don't run the TV faulty with the white line, as it can burn a permanent image of the line on the tube phospher.)
Cobweb
January 2005