Buy a new set of battery cables. Make sure the ground connections are tight.
Buy a cheap Volt-Ohm-Meter from Harbor Freight. Disconnect the battery and measure the resistance from the battery-end of the red cable to the starter. If it's more than a couple of ohms, the cable is corroded. Measure the resistance from the battery-end of the black cable to the starter motor case. If more than a couple of ohms, track back to find the bad connection / cable.
Good luck!