When you're dealing with a flyback transformer that generates enough voltage/current to bring down a horse, I'd suggest not monkeying around with it.
Oftentimes primary rectification diodes can go bad in a TV, since they are the first components after the power enters the case. If you've already gone into the case, take a look at the board for blown components.
Just remember this...
You don't know the charge status of the tube, and without trying to tell you how to discharge the tube, just make sure that if you do get near the components, only use one hand. You want to avoid completeing a circuit across your chest with both hands.
So, yeah, look for small black cylinders with a silver ring around one end. If they appear blown, or there is a good amount of tar/smoke that has stained the board, you may be looking at a blown diode.
Other than that, you could have another repairman look at the TV, find a authorized RCA repairman, though cost may be near replacement cost.
On another side note, check with a highschool Vo-tech class that might be able to repair your TV for the price of parts, hell, thats how I learned to fix stuff.
-SF