setPriority isn't static

I can get a list of all existing threads. I can get their names, their
priorities,
if they are daemon threads or not etc.
To change a threads priority you have to specify which one. I don't see how
it matters if the thread has been started or not.

setPriority only affects the priority of the Thread instance on which
the method was called. It does not change the priority of the thread
that is executing the setPriority method, unless of course, the
executing thread is the same thread as the Thread instance on which the
method was called.

It doesn't matter if the Thread instance is "new" (i.e. just created, or
being created) or if the Thread instance is already running.

The following class shows your example case:

public class MyThread extends Thread {
   public MyThread(int prio, Runnable target) {
      super(target); // invoke constructor of parent
      this.setPriority(prio); // change priority *in constructor*
   }
   private static void print(String msg, Thread t) {
      System.out.print(msg);
      System.out.print("\t prio=");
      System.out.print(t.getPriority());
      System.out.print("\t alive=");
      System.out.print(t.isAlive());
      System.out.println();
   }
   public static void main(String[] args) throws Exception {
      final Thread mainThread = Thread.currentThread();
      final MyThread myThread = new MyThread(Thread.MIN_PRIORITY,
            new Runnable() {
               public void run() {
                  print("Running\t main thread", mainThread);
                  print("Running\t my thread", Thread.currentThread());
               }
            });
      print("Before\t main thread", mainThread);
      print("Before\t my thread", myThread);

      myThread.start(); // starts myThread
      myThread.join(); // wait until myTread ends

      print("After\t main thread", mainThread);
      print("After\t my thread", myThread);
   }
}