Here is what i would suggest, replace the positive cable that goes to the starter, disconnect the negative cable from the body and clean the stud or the firewall where it connects and use a wire wheel and clean the area and then re connect it, and if all else fails go through and check the started selinoid, clean the connection of the positive cable and the starter, and if that fails get a marine or RV deep cycle battery and that should work.
good luck with your car.