See if you have brake lights when you hit the brake pedal. If not then I suspect your brake light switch isn't working. That will prevent you from being able to shift out of Park.
Alex
RepairPal Certified shops can diagnose and repair your 2005 Saturn Relay. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.
I literally just had the same problem a couple weeks ago in my 2007 Relay. The shifter moves, but it doesn't catch? It was a shifter cable bushing. $15 fix & very easy to replace.
thanks will try