If I understand you correctly, it sounds like the solenoid is engaging the starter drive but your starter is not cranking. As dblack1 advised, check the connections from the battery to the starter, specifically the positive cable from the battery to the starter terminal and the negative cable from the battery to the block. If these are clean and tight and the problem persists, you probably need a new starter.
To change it, you will need to raise and safely support the car. Disconnect the negative battery cable. Remove the big plastic splash shield (10mm and 5/16" bolt heads) Remove the flywheel cover (10mm bolt heads). Undo the little solenoid wire on the starter (5/16") and the positive battery cable (5/8") and the two big bolts that hold the starter up to the block (15mm bolt heads). Make note of any shims that are used between the starter and the block. When you install the new starter, keep the surfaces between the starter and the block clean. The starter'* ground connection is made there. The starter should come with a few shims. These are used to reduce the depth at which the starter gear engages the ring gear on your flex plate. If your starter is making a straining noise or is very loud, the gear mesh is probably too tight and shims should be added. If you don't shim it properly, the starter can be quickly ruined.