Go to receive money and select them both -- it will be a ZERO transaction to apply the pre-payment to the invoice.

When I go to Receive Money neither transaction shows on the screen.

Try doing a new test prepayment for the same customer and then a new invoice and check to see if they are visible under receive money.  If they are then you're doing the process correctly so I'd check the data entry on the "missing" transactions because it's either a data entry error or the data is corrupt.  Don't forget to go back and delete your test transactions.

First I enter the customer deposit by going to receive $ and checking the box that says  prepayment. Then I open a sales order. Then I invoice and apply the invoice to the sales order. At this point, when I go into Receive Money, the invoice appears but when I check the box to pay it, it pays a negative amount, and then the customers balance is wrong.

You will need to add an invoice number to the invoice, and a reference number to the pre-payment. Once this has done then you will see both transactions on the receive money screen.

As I understand, we have to check the box for pre-payment right? What is the best explanation whu that box cannot be checked sometimes?

If you have already selected an invoice to be paid you cannot select the pre-payment check box.  The pre-payment check box is meant to be a separate transaction that can be later applied to an open invoice.  

We have found that you can open customer management - locate the prepayment - open it - then unclick prepayment and go to the invoice list - select the correct invoice and apply.   Always double check that the amount is the same before saving.    

And after you see "both transactions on the receive money screen" how do you apply it to the invoice?