this is usually a line contactor problem. and it can be a line contactor problem that is caused by a faulty ecu. the contactor pulls in at battery voltage and holds at a much lower voltage. if the pull in voltage doesn't happen the contactor doesnt lock in and all of the problems you are having can happen. push the arm on the contactor, if it pulls in and locks it might be an ecu problem. you can get creative with a relay and a capacitor but........modifications can be a legal liability nightmare