There are too many variables to give you a definitive answer. But first step is to ask the Association for the name of the insurance carrier and the policy number. Then start shopping for attorneys to prepare and submit the claim in its proper form to the carrior.
DO NOT RELY UPON ANYTHING YOU READ ON THE INTERNET AS THE SOLE SOURCE OF INFORMATION AS TO HOW TO DEAL WITH YOUR LEGAL PROBLEMS. The information provided here is not intended to constitute legal advice and is purely based upon the limited information provided by the inquirer. I urge each of you to seek out an attorney in your community who is familiar with your local court's requirements and practices that will sit down with you and help you formulate a financial strategy which suits the needs of you and your family. In many cases the consultation is absolutely FREE. It is only when we attorneys can meet you and ask all the questions we need to ask that we can fully advise you of your options.
You are right to press on with the issue. If you are correct that the backup was the fault of the HOA then they are liable to you for your damages. I suggest you find a local attorney who works in that field. Good Luck