I have a sharp LC-42CT2E TV which will not turn on. I have turned the tv off with the switch on the tv and at the socket. When the power is connected the led white light at the front of the tv comes on for about 10 seconds and then flashes constantly. The tv does not come on when presing the "on" button on the remote or the tv

SOURCE: Sharp LC-26D43U Power light flashes and unit won't turn on?

It's a power supply related problem. When it turns itself off, this it called protection mode. The TV automatically turns off to protect other parts form being damaged.
The most common problem is the Power Supply Unit or the Backlight Inverter Board.
You may have to take the TV to a repair shop to find out which one is bad. Paying a repair shop to replace the board for you maybe more than the TV is worth. If you let them diagnose it and you replace the bad circuit board yourself, it would be cheaper.

Here's a place I use to get parts for TVs:
http://www.shopjimmy.com/catalogsearch/result/index/?q=LC-26D43U&p=1
The problem is the repair shop may charge you double or three times of what the part costs at the web site link above. Then, plus labor. I just want to save you money. :)

SOURCE: OWNER'S MANUAL AND A REMOTE FOR A SHARP SHARP 46'' TV MODEL lc-46s

The mauual you can get from the internet by Googling it will be in PDF format that you can print. The remote use a Universal cheap GE is good and program with one of these codes....
0079, 0123, 0063, 0020, 0004, 0009, 0226,
0266, 0006, 0095, 0122, Low cost approach.

SOURCE: Re-program a Sharp remote control for LC-46XD1E

Are you sure it is the remote that has stopped working? If you get something like a camera phone and put it over the LED on the remote and press the buttons (with the phone in camera mode) the camera will pick up the infered signal from the remote. This will rule out if it is the TV or remote.

If you get the infered signal then your TV is faulty (possibly a main pcb fault) if you dont then it is your remote. Which as far as I am award you can not reprogram, but you can get them from places on the internet (search on google) for a couple of 10 pound.

SOURCE: LC-42DH77E Sharp No picture Green led comes on

maybe its on power supply try to check at power supply section check nearby parts of regulator ic if you can, test those passive and active parts using vom if those parts are ok then the regulator ic is defective