The resistor is for the ignition coil when running. It should be bypassed when the starter is operating.
Before you do anything else, get a multimeter out and measure battery voltage when cranking. Have to ask the question re: the battery. How new is new? No guarantee that it's still up to snuff to turn the starter over at the proper speed and still provide enough voltage to fire the spark plugs.
Could be the starter as well.
