Every time I try to clear the shuttlecock it just dies into the net. My shots have no power or height. What am I doing wrong?

This is the number one beginner problem and it is almost always about contact point. You are probably hitting the shuttle too low and too far in front of you. Try to make contact higher and slightly behind your head. Imagine you are throwing a ball over the net - your arm action should be similar.

Also check your grip. If you are holding the racket like a frying pan (forehand grip all the time) you will not get the wrist snap needed for power. YouTube has good grip tutorials - look for BG Badminton Academy or Coaching Badminton.

It took me about 2 months before my clears started going to the back of the court consistently. Do not get discouraged! Practice your overhead throwing motion without a racket first - just use a shuttle and throw it high.