RepairPal Certified shops can diagnose and repair your 2009 Cadillac CTS. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.
If you have a second key try that. If not it could be a faulty key fob and a replacement is in order.
Use this link to find a good shop near you.
https://repairpal.com/repair-shops
Alex