I tried making a game loop in Java using the Timer from java.util.Timer. I am unable to get my game loop to execute during the timer tick. Here is an example of this issue.
First of all, Timer.schedule schedules the task for one execution, not for repeated executions. So this program can only make the button move once.
And you have a second problem : all the interactions with swing components should be done in the event dispatch thread, and not in a background thread. Read http://download.oracle.com/javase/6/docs/api/javax/swing/package-summary.html#threading for more details. Use a javax.swing.Timer to perform swing actions at repeated intervals.