Find the starter solenoid and tap on it. It may be in the fuze box, may be elsewhere. Consult your chiltons or manufacturer service manual for the exact location, or if you know what it looks like just start looking for it upstream of the starter wiring.
You can also check various fuses in the fusebox. I had a strange problem with my G8 where trying to start the car would blow the starter fuse. Towed it to the dealer and they couldn't duplicate the problem, but they swapped out the starter under warranty. I suspect they nicked the starter wiring or damaged the starter when they replaced the rear main seal a few months earlier (also under warranty) but they wouldn't admit to finding any damage so who knows.
Still, it could be a lot of things from low battery voltage to a bad solenoid. Battery voltage ought to be in the neighborhood of 23 to 25 volts with no load, but that will only tell you if the battery is not outright dead or damaged. A degraded battery may show 23+ volts with no load but may sag below the voltage required to run the starter once the circuit is closed. Still, it sounds to me like the starter solenoid is not functioning for some reason. Could be a fault in the starter wiring, a bad solenoid, a bad fuse, a bad starter, or a bad battery.