Same thing happened to my 43W809C recently, but it was just the external power supply.
First thing to do, is to take a multimeter (even a cheap basic one will do), and with the external power supply disconnected from the TV (but connected to the wall plug of course!) check if it is supplying a reasonable DC voltage (between 19 and 20 V from the external metal part of the plug/pin that goes into the TV and the interior).
If the issue is simply that the external power supply is no longer supplying the correct voltage (or if it's completely dead), just buy another one. Hint: there are some universal ones that come with a wide array of replacement pins and and several selectable voltages. Just check that the power rating (W) is at least as high as that of the official supply, and you'll be fine spending MUCH less than for an original Sony replacement.
