Car will not crank over, battery?

This Caprice is an ex-police cop car. My son left for the Navy and asked me to sell it. Two days after shipping off to basic in Great Lakes Illinois, it will not start. I put the key in and turn the ignition on to start it and nothing, no click, nothing. Dash lights come on, headlights turn on. I cleaned all the negative ground connections from the battery to the starter and ground straps. The battery is 2 months old. My presumption is the starter and or the starter solenoid. Since I am not sure, how do I test the starter, the starter relay (presuming I can find it) and or the ignition switch. Thanks in advance for your help.