This is often caused by failing or failed capacitors in the power supply unit (PSU). In my case I had a Lexsor 32 inch LCD flat screen (psu part number KAS200-5S241812XS VER A2.1) but these notes probably also apply to any number of similar LCD flat screen TVs with similar problems. Make sure and double check the values of any components you replace against your own TV's. The component values I have given are just for my make and model of TV.
Naturally these instructions should only be used by fully competent persons who know what they are doing and anything you do is entirely at your own risk. If you do not feel competent to look inside your TV and do the repairs yourself then maybe consider printing these notes and giving them together with your TV to a fully qualified and certified TV repair specialist.
Here's what happened to my TV and how I fixed it:
The blue front light came on when my TV was turned on but there was no display or sound. Sometimes repeatedly pressing the on/off button many times finally got the TV to turn on but it made a buzzing / hissing / static crackly noise and it took many minutes until the LCD display and sound came to life. Eventually even repeatedly pressing the on/off button failed to work and only the blue light on the front panel came on with no other activity.CAUTION:
MAKE SURE YOUR TV IS UNPLUGGED FROM THE MAINS AND *NOTE* THERE ARE VERY HIGH VOLTAGES THAT MAY STILL BE PRESENT INSIDE THE TV EVEN AFTER IT IS SWITCHED OFF AND UNPLUGGED FROM THE MINS POWER SOCKET. TAKE VERY GREAT CARE NOT TO RECEIVE AN ELECTRIC SHOCK. MAKE SURE YOU REALLY KNOW WHAT YOU ARE DOING *BEFORE YOU DO ANYTHING*!
I opened the TV and located the PSU board (see photo). Six of the electrolytic capacitors were clearly puffed at the top (your TV may have a different number of capacitors that need replacing). They should all have flat tops so if they look "puffed up" (a bit like a bottle of fizzy pop that's been shaken) then they need replacing.
Please note that in my PSU three of the capacitors were orange 25v 680uF electrolytic radials and three were black 35v 680uF electrolytic radials. I un-soldered the capacitors from the board and replaced them all with 35v black 680 uF electrolytic capacitors (I reckon the few extra pence the 35v ones cost instead of the 25v ones is money well spent!)
Re-assemble the whole thing and - there you go - I hope you are as lucky as me and your TV is as good (or better) than new!