I don't have the knowledge to help you but I don't know to what extent doing two draw() functions nested help. Moreover, 

draw = function() {
if (keyIsPressed) {
if (keyCode === 38){
movePlayer1Up(); }
else if (keyCode === 40){
movePlayer1Down(); }
}

So what I want to say here is that the else if should be going inside the second if statement. Another problem I see with your code is the repeated (again) use of conditionals. Try to avoid that. Not very familiar with the syntax either so I won't be of much help. Good luck. 

Let's take a look at the HINT code:

draw = function() {
    if (_____) { <= needs a condition; yours is good
        if (keyCode === _____){ <= there is a STRONG clue in the instructions
            _____(); <= a function; look closely at the exact names of the
                        functions that are already defined in the starter code
        }
        else if (keyCode === ____) { <= Again, STRONG clue in the instructions
            _____(); <= another function; again, look at the exact names of
                        functions defined in the program
        }
    } 
};

NOTE: You should really never to assign more than one function to the draw variable in any program.  If you assign a second function to draw, that will over-write the first function you assigned to draw.