If you don't know how to diagnose and repair delicate electronics, i would leave this up to the pros because you could end up hurting yourself or do more damage!
The cheapest/best way to go about this is to take the board in question to a repair shop and have them repair it!
I'm guessing the problem lies on the Main Input or Power Supply board(or maybe both). A bad resistor will discolor the circuit board around it. On-board resistors cannot be replaced! They can only be bypassed(jumped) or replace the whole board!
Capacitors look like mini pop cans...usually black. They can blow and will have a bulged top, leak from their top or bottom OR so no signs at all! In which case, only testing the circuit they are on will tell if they're bad or not!
Pic of blown capacitor: http://gallery.techarena.in/data/519/bad_cap.jpg
If you can't find any damage, you'll need to take the whole TV in for repair. Or the two boards that i mentioned, at the very least!
Good luck.