I don't know about your component cables but I can tell you a few things about the flyback transformer in your set. This is the component that is responsible for generating the 32,000 volts or so that your picture tube requires to display the picture. It also powers other systems in your TV.

These transformers are a short circuit waiting to happen. They're wound from very thin wire with thin insulation. The wire is practically invisible and it's wound into tens of layers with thousands of turns. If you breathe on this wire you're likely to break it because it's thinner than human hair. The whole thing is then potted with a resin. Any imperfections in the insulation or trapped air bubbles in the resin, coupled with the intense thermal stress that they are under, can cause these things to fail. So I am not surprised that it's toast.

You'll want to assure yourself that the repair place knows what it's doing. If they solder a new transformer in and apply too much heat to it during the installation process, they can significantly decrease its life. Ditto for the electronics unless they replace the whole board. And I presume for that price they will not attempt to re-wind the transformer which would be absolute lunacy.

If you decide to go through with this, try to get at least a three month warranty. Good luck.