Something similar happened to my 2008 ZR6 the other day at the video store. Pushed the button, everything lit up as usual, heard this rapid clicking sound. I did think my starter was bust, luckily the storage yard for the local towies was next door and he offered to tow me, but then we decided to see if it was a flat battery. The horn and lights actually still worked so I thought it was the starter....anyway, brings over the portable jumper and surprise surprise, car starts first push of the button. So try jump starting the car, see if that works. If not, try a new battery?