I had some problems with my arduino kit with LCD Type 1602 (1602a).
For all newbies (like me ):
In most cases your LCD is not dead.
Is your backlight working?
Check if you can control your contrast correctly. If you can control it from seeing nothing to
see white blocks you are on the right way. (if you see white blocks step down just a little bit till you see shadow of the blocks.)
check your cables! test them with a multimeter and check if they are working correctly.
(or just connect + and - to LCD backlight and change one of the cables)
If you have the big breadboard (60pin) (THIS WAS MY PROBLEM):
If you have a starter kit with a big (60 pin) breadboard - there is a break of the + and - line near pin 30!
So when you connect your power from arduino to + and - on the left - you have this power just on pins 1-29!
This was my problem. I had connected some of the pins to the left but one or some of the right pins were connected to the line which was not bridged to + and -.
Check the pins connected to the board / LCD and check the sketch settings. First try a tutorial with the default settings and default wirering.
Other libraries may help but you need more informations about the exact type of your LCD.
If you have a LCD type 1602 (most starter kits) and you have 16 pins, you can use the default tutorials.
if you have the same display, but you have an LCD with a second pcb which has 4 pins you can use it with "i2c" libs.
Hope that I can help some people who have the same problems with their LCDs