What would cause my car not to start
with a new battery, new coil, new
plugs and wires
What testing have you done? Make sure battery has a full charge and connections all good. If it cranks good but won't start, have a helper crank it while you check for spark at the plugs, visually. Use a gage and check proper fuel pressure and fuel injector pulse. Check applicable trouble codes. Those are the basic checks in my opinion. Check for rpm signal, some Chrysler vehicles the computer has to see both cam and crank sensor signals or it won't start. Now, if your saying the starter motor won't even crank the engine, that is a different issue.
You have to start with some good old fashioned troubleshooting. Is the engine turning over (cranking)? If Yes, the battery and starter are good. Does it have spark? Pull a plug wire and test. If not, you have an ignition system problem. Does it have fuel? Starting fluid is the easiest way to check (remove air filter and spray a bit in to see if it starts). Does it have timing or compression? Could be a broken timing belt.