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If there's enough corrosion material to affect the connection between the cable and the terminal, forget cleaning it off. It's time to replace the battery.
If it's not the battery, there are some safety lockouts that will prevent the car from starting.
Many manual transmission cars will not crank if the clutch is not depressed (but that would be obvious as you have owned the car for a while).
Automatics will not start unless the transmission is securely in "park". If it's not there's an interlink that prevents the starter motor from engaging.