Sounds like the starter solenoid is bad also
Check the battery cables for looseness and/or corrosion A weak battery or coroded, loose,or broken cables on/from battery to starter or engine ground will cause a starter selinoid to click without turning the starter. Less often, the windings in the starter or the brushes may be worn out, requiring a replacement. Salt deposit or corossion on the starter lugs also may rob power to the starter. It is VERY IMPORTANT to remove the negative battery cable first, before cleaning, removing or servicing the positive cable on the battery or the starter to avoid possible arcing or shorting battery voltage.