Hello SeanH and welcome to the Community.
Home Depot does offers a military discount to all active and veterans of the United States Military. So, you were misinformed, if someone said you are not eligible. Unfortunately Home Depot Online Line order do not offer military discounts ( except for special days) and a few specific products that are not discounted. Home Depot wants to show you the appreciation you deserve, for your service. If you have further difficulties at your local Home Depot, please enlist the assistance of the manager.
Thank you for your service.
Charlotte of the Home Depot Community.