How do you fix a Sharp LCD LC40LE810UN that won't power on

Gonna cost u mor to fix then a new one at wal*

Try to I unpluged the power, push volume and channel down, pluged power again

While it's flashing unplug your TV from the main power source for 15 seconds,Then press Valume Up and Channel Up, while holding it plug the TV back in, you should see the TV Turn on. How to Reset Your Sharp LCD TV TV Repair

CHANGE IC202 WITH TL431 OR TRY PUSH INPUT AND VOLUME DOWN THEN PLUG THE POWER UNTIL THE GREEN LIGHT START ,,, WHEN IT START PUSH VOL DOWN AND CHANNEL DOWN AT THE SAME TIME AND PLAY WITH THE SETTING

The clicking sound may be a power relay coming on and then off--problem indicates a trouble in the main power supply.

power supply which can be ruled out or confirmed with voltage checks on that board.

Try to check the main line and if its ok proceed to the power chord then to transformer or the fuse and you look it they are fine look for a technician to check your tv.Choose a better technician near from your place.

try checking the system for timer or sleep mode operation try to setting it off

did you check to see if one of the buttons on the remote is stuck down?

Sound like the TV is in protection mode. This happens when a part goes bad inside. the TV turns OFF to protect the other parts from being damaged.
Most commonly it's a power supply related issue. A bad capacitor or transformer on the power supply board is to blame.
For a do-it-yourself fixer with electronic experience, a Service Manual is the best for trouble shooting the problem down to the bad part. Normally, you can find it over the internet for less than $20.