Yes, double-checking every connection is a very good idea - it only takes one thing wrong to
stop things working, and usually there are a lot of things to get right.
You saw the comment on that page about the Wire library?
The LCD might be broken or the sketch could be wrong. Is the Arduino LiquidCrystal library used, or an own library ?
Could you try an example of the Arduino LiquidCrystal library ? The "HelloWorld" example is one of the examples that is already in the Arduino IDE.