Technical advise

Sure. First, check the battery voltage with a multimeter—should read twelve point six volts. If it drops below ten point six volts during cranking, that's a problem. 

Second, verify your grounds. Use the remote start switch—clip one to the negative on the battery and the other to a clean spot on the engine block. and try to start the car. If it cranks, the ground's solid. 

Put the broken end of a fishing pole on the ignition coil and try to crank the car. If it vibrates, the coil is functioning.