therealone:
Thanks for the answer! Two questions though:1.) Do I have to solder the pins the the LCD? Doesnt it get contact otherwise?
2.) I tried a 2.5kOhm resistor and a 10kOhm resistor so far. A Resistor does the same thing as a potentiometer, only it has a fixed value, right?
Yes, you solder the pins on. No alternatives.
A potentiometer is a variable resistor. You can't vary those cylindrical resistors that you are currently using. If you are in a hurry, go to a local radio shack store and get a potentiometer anywhere between 2k and 20k. Otherwise, get a pack from ebay.
Also, put your location information in your profile. Some people can give you location-specific information. Like I can tell you where to get parts locally cheap if you are in my area.