I'd put money on it being the physical ignition switch located behind the key cylinder in your car's steering column. That would explain why it would take 2-4 turns of the key to turn the engine over. As a side note, accessories like lights and the radio working does not essentially mean your battery is fine. Those devices put a very small load on the battery and often will operate even if the battery is "dead" (won't crank the engine). The only real ways to check if the battery is dead is to use a bump switch as said above or to buy a load tester, which is essentially a giant resistor that puts a large load on the battery similar to that experienced when the starter is cranking the engine. Multimeters don't put a big enough load on the battery to tell if it is good or not. They can be found at harbor freight for the cheap.

Probably. See if you can find a mechanics "bump" switch and see if you can turn the motor over with that. If so you probably have a problem with your ignition switch. Those are readily available and usually not to expensive. Ralph

Or use a voltage tester,(on DC that is) on the battery and check to see if you have 14 volts. If you do then its fine.