That's not a "C" convertible. Have you tried following the start procedure after the car has sat more than a few weeks? The multiair cylinder head drains it's oil after a few weeks. You have to connect a charger and crank the engine like 25-30 times for about 10-15 seconds each time allowing the starter to cool in between so you don't burn it up. This allows air to purge and 300psi oil pressure to build up so it can actuate the intake valves. I hear if you remove the oil cap and press on the metal ball on the right side it's easier to purge air. (I haven't done this.) This engine only uses a camshaft for the exhaust valves.
I'd probably change the oil as this engine is highly dependent on super clean oil to actuate those intake valves.
Since you live in an extremely hot climate I'd use only full synthetic oil. The spark plugs are supposed to be changed at 30,000 miles so I'd get factory Mopar plugs.