Hello, make sure you are using a properly programmed key to start your vehicle. A key issue could cause a start and then stall. Also check for engine performance concerns. It is possible that a fuel delivery problem or ignition system problem could cause a start and stall. Only hands-on testing will reveal what is going on with your vehicle.
Use this link to find some shops near you that can help with your concern:
www.repairpal.com/repair-shops
RepairPal Certified shops can diagnose and repair your 1996 Buick Regal. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.