Just self repair a Sammy 32" LCD tv last week which is older than your due to a faulty power supply board. If you are sure or suspect that the power supply board cause tv cannot turn on, you may try open the back cover (disconnect power cable 1st) and look out for the part number of the power supply board. I not sure your tv back cover is easy to remove or not but mine not difficult. Then go taobao to search for the exact board for price and decide yourself whether worth to get it and DIY or not. Anyway 死马当活马医 so you may want to give a try. But of course, do it at your own risk.
For my case I first check the fuse on the board and found faulty. After changing a new fuse and power on, the fuse immediately blow off but I can see the Power led on a few second and off again. Lucky to found a exact board and bought it for replacement. Now the tv is working as usual and the damage is less than your budget for repair. Good luck.
Should be due to bad capacitor.