Won't power up

If still under warranty or if you have no electronic repair experience you should take the set back to the shop or to a repair person. Some of the solutions described below can be dangerous, TV's are very hazardous to service. Even when plugged out, TV's can store very high voltages.

There are many things in the set that can fail, and cause it to not start.
The set would have to be properly troubleshooted.

If you still want to have a go at it, here are a few suggestions:

check for bad connections near the mains input, and main switch
continuity - wear and tear on the switch (and/or its soldering) may
have taken their toll.

could be a cold solder.

bad capacitors in the power supply are
likely.

Most small tv's have small glass fuses (like the older cars)
if it won't power up that is usually the problem.

If all else fails pull the power cord for a week and then try.

Good luck, Take care