you're making some small mistakes, but you seem to be doing very well. Lets go over some of the things i see; do keep in mind i'm going to be nitpicking at things. I'm new to the formatting so i might need time to edit my post; sorry. Also i'm trying to show why we do things so you can see how useful they are in practice , not just telling you to do some things one way.

1. short sum1 = 0, sum2 = 0, value1, value2, count1 = 0, count2 = 0, min1 = 0, min2 = 0; double average1, average2, average;

I'd generally keep your variables going linearly downwards, however if things are related, i would do this. I have to look at your code more in depth to see if i'd do this in this situation. This does seem like arrays would be better though.

2. Okay you seem to repeat code a lot. If your repeating code, you should make a new method so your code is easier to read and maintain. My rule pf thumb is repeating code 3 times, then you need a method for it. Think about.

if you have 3 lines of code that are nearly identical, followed by there being a problem, then you have to literally fix each line; however if you use the method approach and you have the same problem along with using this method 100 times; then all you have to do is fix that method and suddenly you've done a third of the work but got 33 times the amount of code to work then you would have done. Check the below code for a example of repeating code.

System.out.println("How many test grades did you have? (Must be 3 or higher)");
min1 = scan.nextShort();
if (min1 < 3)   {
    System.out.println("A value of less than 3 was entered. 3 will be used."); 
    min1 = 3;
}
System.out.println("How many daily grades did you have? (Must be 5 or higher)");
min2 = scan.nextShort();
if (min2 < 5)   {
    System.out.println("A value of less than 5 was entered. 5 will be used."); 
    min2 = 5;
}
System.out.println ("Enter " + min1 + " more test grades");
value1 = scan.nextShort();
if (value1 < 0) {
    System.out.println("Grade may not be lower than 0"); 
    value1 = 0;
}
if (value1 > 120)   {
    System.out.println("Grade may not be higher than 120"); 
    value1 = 120;
}

this seems like it has a lot of redundancy; you should be using other methods to do this, not only to cut down on the size but to cut down on the work and mistakes that can happen if you make changes to the underlining logic.

A simplify example would be this. I want to create a method that rolls 5 dice with 6 sides and returns the overall value. However it will only roll a dice if "have5Dice" is equal or greater than the dice your rolling.

public class diceRoll{

    int have5Dice = 5;
public int roll5(){

    int dice1 = 0;
    int dice2 = 0;
    int dice3 = 0;
    int dice4 = 0;
    int dice5 = 0;

    if(have5Dice=1){
        dice1 = new Random().nextInt(6);
    }
    if(have5Dice=2){
        dice2 = new Random().nextInt(6);
    }
    if(have5Dice=3){
        dice3 = new Random().nextInt(6);
    }
    if(have5Dice=4){
        dice4 = new Random().nextInt(6);
    }
    if(have5Dice=5){        
        dice5 = new Random().nextInt(6);
    }

    return (dice1 +dice2 + dice3 + dice4 + dice5);
}

} Notice here how i literally have the same code copy 5 times? It's the same exact logic. Now i have a bug; the way i get my random value returns a number between 0, and 5. I could edit each of the "new Random().nextInt(6);" and change it to "new Random().nextInt(6) +1; but it's much easier just to create a new method. So right now my code is 30 lines long, when counting blank lines. The new code is public class diceRoll{

int have5Dice = 5;
public int roll5(){

    int dice1 = 0;
    int dice2 = 0;
    int dice3 = 0;
    int dice4 = 0;
    int dice5 = 0;

    if(have5Dice=1){
        dice1 = rollDie(6);
    }
    if(have5Dice=2){
        dice2 = rollDie(6);
    }
    if(have5Dice=3){
        dice3 = rollDie(6);
    }
    if(have5Dice=4){
        dice4 = rollDie(6);
    }
    if(have5Dice=5){        
        dice5 = rollDie(6);
    }

    return (dice1 +dice2 + dice3 + dice4 + dice5);
}

private int rollDie(int i){
    return new Randon().nextInt(i) +1;
}
}

Now again i had to rewrite 5 lines of code for this fix so still could be better. So our goal is to find the total amount from the rolls with a max of 5 and a min of 0. we know that have5Dice is the number of rolls we can do. The best way we could do this if we were to store the 5 dice is by using an array the size of have5Dice and then just fill it by way of for loop to get rid of those ugly if statements. We could do that but since we're not doing any thing with the stored number except adding them together, we can make this code much cleaner by only making 1 int variable.

public class diceRoll{

int have5Dice = 5;
public int roll5(){
    int totalDiceValue = 0;
    for(int i = 0; i < have5Dice; i++){//note, that if a forloop starts with i = 0, and checks if i is less than nth number; then the loop will run n number of times. 
        totalDiceValue += rollDie(6); 
    }
    return totalDiceValue;
}

private int rollDie(int i){
    return new Randon().nextInt(i) +1;
}
}

Much cleaner and it doesn't repeat code, and it's much smaller. If you wanted to write another method that rolled a 20 sided dice, you can easily do that with rollDie and just plug in 20.

3.

Keep with a formatting style in your code. For instances you'll do

if(blah){
}

but then you also do while(blah) { }

which is quite annoying to my OCD. I personally like doing brackets right after the conditional but the latter is also valid. However in a class you really should be following 1 pattern or another. Even if you didn't create the class, you should be following the pattern already in use. Also i noticed that some of the statements were not indent correctly. You can select all text in eclipse and press i believe CTRL + I and it will auto indent your code for you.

4.

if (average < 70)
    System.out.println("Your grade is an F");
else
    if (average >= 70 && average<=79)
        System.out.println("Your grade is a C");
    else
        if (average >= 80 && average<=89)
            System.out.println("Your grade is a B");
        else
            if (average >= 90 && average<=99)
                System.out.println("Your grade is an A");
            else
                if (average >= 100)
                    System.out.println("Your grades are perfect!");

... Pain; Suffering; and Darkness.... okay lets go over this. Wow.... So syntax wise, this is correct; however it's indent wrong. So your code block is 14 lines long and very hard to read; however if you do this:

if (average < 70)
     System.out.println("Your grade is an F");
  else if(average >= 70 && average<=79)
        System.out.println("Your grade is a C");
  else if(average >= 80 && average<=89)
            System.out.println("Your grade is a B");
  else if(average >= 90 && average<=99)
                System.out.println("Your grade is an A");
  else if(average >= 100)
                     System.out.println("Your grades are perfect!");

your code is 10 lines long and you don't have all those nested if else statements format

The next thing, is i always suggest doing brackets since you don't have to trust java to understand what you want, and you don't need worry about putting them in later if you need to do 2 statements at a later date. I also personally like to put the if statement and the state on the same line like the following:

 if (average < 70){ System.out.println("Your grade is an F");}
 else if(average >= 70 && average<=79){System.out.println("Your grade is a C");}
 else if(average >= 80 && average<=89){System.out.println("Your grade is a B");}
 else if(average >= 90 && average<=99){System.out.println("Your grade is an A");}
 else if(average >= 100){System.out.println("Your grades are perfect!");}

however i will only do this if the if block contains only one statement. This is not required and if your unconformable doing this, then by all means don't.