This is a common fault to most of the CRT based [picture tube based] televisions. As we switch the set ON, by its power ON/OFF switch, the standby LED light once and the set turns fully Off state.
In most modern televisions, the main system control IC is so programmed that, as soon as it detects a short circuit in the main board, the IC will detect the situation, and sill send a stop signal to main power regulator section to switch the entire system OFF. This is a protection process.
The main cause for this fault is with the horizontal output section of the set. To make it sure, just disconnect the B+ power supply rail [usually come between 90 to 130VDC]. Connect a filament type bulb in series with this line to ground. Use a 100W bulb. Switch on the TV at this condition. If the bulb shows a glow, and stays lit, measure the voltage between the main B+ to earth. If it is almost OK, make sure that the horizontal output section has the fault. If the bulb does not glow at all, make sure that the fault is with the missing B+DC line. Check for it.
If the bulb glows constantly, and when you connect the B+ line, the power supply switches OFF after a moment, concentrate on horizontal output section. There are three components to be suspected. The first one is it LOT [Line Output Transformer], the second one is line output transistor, and the third one is a deflection yoke. Among these, fault to deflection yoke is very rare, almost 1%, we can say. Fault with the horizontal output transistor and LOT are common.
Desolder out the horizontal output transistor from circuit. Switch ON the TV. If standby light stays lit, and B+ voltage is OK. Make sure that the horizontal output transistor is leaky. Leaky means, it will have its internal junction [Collector to Emitter or collector to Base], has shorted.
There are tow reasons for this transistor to get shorted. The first one is of overheat. The second one is with some shorted extra high tension windings inside the LOT.
To make sure about which one caused, just solder a new horizontal output transistor in place, Switch On the set for a short time, say about 5 seconds or so. Switch Off the set. Unplug it from wall power outlet. Feel the heat of the newly soldered horizontal output transistor with bare fingers. It should be slight warm, but must not get so much heated at this short period of time. If it heats up abnormally, the LOT has the fault, and it should also be replace with same type and number