92 PA start up problems

Sometimes when I go to start it up it will start with no problems and sometimes it does not want to. All the lights comes on. the starter does not roll. But will start normal if I wait 15-30 min. My car was leaking water from the truck and I did not notice and the car sat for a week and it was hot outside so the moisture was all over in there. It has fairly new battery and alternator. Should I go Starter or ignition switch etc. Never had to change starter. Had car for 5 years. THANKS

when it wont start wiggle your battery connections if still nothing then tap on starter with hammer not to hard though if it starts with the wiggling of the cables you got a bad connection if the tapping on the starter does the trick you have a bad starter