Character Sprint Spaghetti Code
From a once over


Indentation is terrible, consider using a tool like jsbeautifier.org, it works for ActionScript as well
Keep working with Event.ENTER_FRAME &lt;- It is the better approach in my mind
Always be on the look out for copy pasted code, this:

if (sprint) {
  timerStart = false;
  condition1 = false;
  condition2 = false;
  sprint = false;
  timer = 7;
}

if (timer &lt;= 0) {
  timerStart = false;
  condition1 = false;
  condition2 = false;
  sprint = false;
  timer = 7;
}



could be 

    if (sprint || timer &lt;= 0) {
      timerStart = false;
      condition1 = false;
      condition2 = false;
      sprint = false;
      timer = 7;
    }



Do not track keyDown, you do not use it, and it's value is always the opposite of keyUp
condition1 and condition2 are very unfortunate names, you should try to be more descriptive 
This code could use some well named constants and indenting:

if (sprint) {
player.x += 7;
} else player.x += 2;


I would rather see

var FAST_SPEED = 7,
    NORMAL_SPEED = 2;
if (isSprinting) {
    player.x += FAST_SPEED;
} else {
    player.x += NORMAL_SPEED;
}


or if I wanted to be fancy 

player.x += isSprinting ? FAST_SPEED : NORMAL_SPEED;