Disconnect power supply and take rear cover off. The boards.. Usually 3, will have part numbers on them. Take a look for any bulging or leaking capacitors (brownish gunge running downwards) you can try desoldering and replacing those caps or buy the entire board they are on. Cap replacement is the cheapest option. buying a board from eBay or similar can be done easily.. I bought 3 boards for 1 tv and none worked! They tend to be taken from other broken tvs! Just check feedback and returns policy first. I'd never fixed a tv before and found it fairly straight forward. Just take your time, use a camera to take photos along the way so you know how to reassemble.btw.
Depending on where you live, try one of these areas on PartsIn.com:
It mainly aggregates classified ads, so you never know. You might get lucky and score exactly what you need for real cheap. You usually have the option to haggle with them because often the sellers don't find a buyer and they just end up throwing it out anyways.