First THOROUGHLY check the battery cables at both ends for perfect connections. Corrosion down a cable is like a water hose with many leaks. "Juice" to your starter and especially at startup is essential. Very, very ofen poor cables are as at fault as a poor battery.
Second, check for voltage at the starter. While someone turns the ignition switch to the start position see if the starter is even getting anything. Could be the switch mechanism on the column.
You have to see where the open is and this is one of the first places to begin. The starter solenoid could be the culprit. But verify, before you replace anything.
You might also try starting the vehicle in "neutral." If the starter won't turn over, it COULD be the neutral safety switch. If the starter does turn over in neutral, the shift linkage probably needs adjusting.