Brian Green this does sound like a seized engine. First off “I can push the car in drive and reverse “ will not turn the engine at all so it does not fator in your troubleshooting. Remove all the plugs and then try to turn the engine over by attaching a socket and breakerbar to the crank pulley. If you cannot you most likely have a seized engine. The reason why the starter cable gets hot is because of the amperage your starter is drawing trying to crank the engine over. Let us know the exact make and model of your vehicle as well as the year and engine size so we can try to help you further.