First, fully charge the battery. Then short across the two large lugs of the solenoid with a big screwdriver (ignore the sparks). Does the starter turn now?
If not, it could be battery or connections to the battery. Measure battery voltage when pressing the start button. If below 9-10V or so, the battery may be the problem (not fully charged or bad). If above 10V, then measure at the output of the solenoid where the cable goes to the starter, again, when pressing the start button.. what is it? If 9-10 or above, then measure down at the cable lug on the starter. What is it? If 9-10 or above, the starter is somehow being kept from turning - bad starter, siezed motor, etc. If below, there's too much drop in the cable.
Following the above measurements (all made while pressing the start button), find where voltage drops significantly, this will tell you which cable (if any) is damaged.