Hello. Welcome to Just Answer. Please allow me to assist you
The P0420 is usually a cat code, and the P0300 is a multi-cylinder misfire.
Neither of these codes will cause the engine
to not start.
You need to determine which system is causing this.
First, remove a coil pack and crank the engine. See if you have spark.
Second, Loosen the line at the injector rail of fuel filter. When cranking, fuel should squirt out.
Third, get a NOID light from your auto parts store. Disconnet a fuel injector wire connector. Attach the Noid tool to the fuel injector wire connector. It should blink when cranking
First test: You should have spark. No spark? Check all fuses under the hood and under the dash
Second test: No fuel? Verify the fuel pump
third test: No Noid light blinks? you probably need to check the crank sensor where is is bolted to the timing cover.