When you Edit or View the customer, go to the Transaction tab. When viewing Current transactions, you should get a blank screen and no records, either with current balances = 0 or non-zero. If anything is on this screen, you will not be able to delete the customer.

How are you trying to delete the customer? From within A/R or Time&Billing? From Edit Customers or Delete Inactive Customers? It might make a difference, as some methods of deleting customers require not only the Current A/R transactions to be cleared, but also all Historical transactions as well. Some methods of deleting customers do not require purging the customer history beforehand.