Led power light comes on but screen will not come on.

"Blinks a few times" implies the TV is flashing a fault code at you. If you can find a service manual for your model, count the number of blinks and look it up in the diagnostics section.

However, the most likely problem is a burned-out electrolytic capacitor in the power supply. These are usually easy to identify visually; the top of the can-shaped capacitor should be flat, but may be bulged out and may have brown or black material leaking from the vent scores. The photo below shows a bad capacitor to the right of a good one; both have black plastic sleeves.

If this is the case, replacement capacitors are relatively cheap. However, you should look for the following criteria in choosing a new part:
>Capacitance (uF): same as the original, or 10% higher if the original value is not available
>Voltage: same or higher
>Temperature: Maximum temperature should be same or higher
>Physical size: should fit in the space occupied by the original; if buying a taller unit, make sure it will fit when the back cover is reinstalled, and make sure the capacitor will not touch heat generating parts such as heat sinks, resistors or large transistors.
>Ripple current: get the highest available without compromising too much on endurance. Ripple current may be specified in mA or A; 1 A = 1000 mA. Sometimes you can get a better rating by going to a higher voltage part, but physical size may be a limitation.
>Endurance: Try to get 8000 hours or better.

I usually use Panasonic FR1 series capacitors, although United Chemi-Con EKZN capacitors are also worth a look.