LCD TV's don't have a bulb. They have backlights (usually compact fluorescent tubes) and a panel of LCD pixels. So you can have one of three things fail: the video board, the inverter that drives the backlights or the backlights themselves. If the problem happened suddenly the inverter is more likely to have failed. As the backlights fail, the screen slowly dims or the image will become pink/red. Look closely at the screen, if you see a dim image then the backlight has probably failed (block the room light but try looking with a flashlight from a few inches away from the screen). If you see nothing, the inverter or the video board are more likely suspect.
For an out-of-warranty TV, open up the back of the TV and remove the shielding. Look for any scorch marks or bulging or damaged capacitors. (Sometimes other parts will fail on this part but these can be spotted easily. Capacitors look like cylinders on a tripod.) The scorch mark and smoke may indicate a resistor or zener diode that had been used as a fuse and is now gone.
If you borrow (or have a) high-end multimeter (able to measure high frequencies - 50 kHz) or an oscilloscope, hold the multimeter probes a fraction of an inch apart about an inch above the inverter board and power up the TV. If you see a 1 or an actual value, you have a good inverter. If you see a reading near 0, the board is bad or the multimeter can't resolve the frequency.
In either case, you can buy a replacement inverter for $50-150 and just do a simple swap. Disconnect all of the wires (connections are similar to molex and ribbon cables in a computer) and remove board (a few screws usually). Connect the cables to the new inverter. (If you google backlight inverter replacement, you'll find videos and text descriptions.) Note the part number on the board, including the Rev number, and order the exact one (shopjimmy.com or lcdparts.net are good starting points). Universal inverters do exist but can result in reversed controls (up to lower the brightness). Replacing individual parts on the board is cheaper but more prone to not tracking down all of the bad parts.
If the inverter is good, then it's probably backlights themselves (several in most TVs). These are sandwiched on the perimeter of the TV (usually under some tape that holds the lamp, reflector and other parts together. You need to order by length and width and get ones for your TV size. Separate the panel from the bezel. Remove the tape, and separate the reflector (make a note of how things are put together) then you have to Dremel (or use another rotary tool) to remove the plastic to get the backlight out. (They are often molded into the frame.) Then put in the new backlight and reassemble everything. (http://www.lcdparts.net/howto/default.aspx
) but for an overview: http://www.inventgeek.com/Projects/BacklightFix/overview.aspx
Then push the new backlights into place, reconnect the wires and close up the sandwich of tape and other parts around the screen. Then replace it in the bezel.
With a good spare backlight, you can test an inverter for condition (plug together and turn on the tv while the box is open). Similarly a good inverter can test the backlight.
I hope this helps.