I have a 1997 grand prix. Most days it starts. once in a while it will not start. You can sometimes rock key back and forth quickly and it will catch. But most of the time odly enough wait over night and it will start on first turn. What do you think it might be.

When you turn the ignition key to start your car, voltage from the battery flows through the ignition switch to the Park/Neutral safety switch and/or brake pedal or clutch pedal safety switch (you have to push the pedal down before the circuit will complete) to the starter relay or solenoid. When the relay or solenoid is energized by voltage from the ignition switch circuit, it closes a contact that routes more power from the battery directly to the starter to crank the engine. The starter motor spins, pushes the starter drive gear to engage the flywheel and cranks the engine.

Low battery (Check battery voltage, recharge if low, or jump start with another vehicle or battery charger).
Loose or corroded battery cables (Inspect, clean and tighten BOTH ends of BOTH battery cables).
Bad starter relay wiring connections or ground connection (Inspect, clean, tighten wiring connections).
Bad starter relay/solenoid (Check for voltage at relay, if relay has voltage but there is no "click" when key is turned to start, replace relay).
Bad starter (Jump battery voltage direct to starter to see if it spins, or remove starter and have it bench tested at auto parts store).
Damaged starter drive or teeth on flywheel (Remove starter and inspect drive gear and flywheel teeth, replace damaged parts if necessary).
Bad ignition switch (Check to see if voltage reaches starter relay/solenoid when turn to start. If not, check for open P/N switch and brake or clutch pedal switch. Replace ignition switch if defective).
Open P/N safety switch, or open Brake Pedal Safety Switch (automatic transmission) or open Clutch Pedal Switch (manual transmission). Bypass switch with jumper wire to see if engine cranks, or use test light or voltmeter to check for voltage passing through switch when ignition is turned to start.
Engine seized due to bearing failure or internal damage (Use socket and long handle to see if engine can be turned by hand, if not engine is locked up).
Engine hydrolocked due to coolant leak from leaky head gasket (Use socket and wrench to see if engine rotates, remove spark plugs and see if coolant comes out or engine can not be cranked with plugs out).