Intermitent starting 2001 Saturn

2001 saturn l-series. Starter does absolutely nothing. Happened once before when wife was using. Went to car. Turned key and vrooom. 3 weeks later I am using car and after a short drive and 5 min stop same problem. All dash lights and systems are functioning properly. Start position>not even a click. Have read that this is a common problem but cannot find a diagnossis for the problem. Currently car is in a shopping parking lot. All connections and terminals look like brand new. Solenoid on starter or elay somewhere? Has anyone ever heard of this problem and actually because it appears to be common, Know the fix before I spend alot of money? I am a collison?Painter with a half a clue but am baffled by this one?