Let's back this thread up a bit before a starter gets needlessly replaced...
Let's talk about your battery first.
How old or young is it? Has it ever gone dead? If it's been dead, how long, and how many times before it was charged back to life?
I ask this, because lead acid batteries will die a horrible sulfated death if they have gone dead for long, or many times. When you charge these damaged batteries up, they may show acceptable voltage (around 12.6V), but will be gutless when it comes to available amperage. You need amperage to get the starter engaged and the motor spinning. If you're unsure about the condition of the battery, most auto parts stores offer free testing to confirm if the battery is good or a core. Even if the battery needs to to be replaced, keep reading...
Next...Battery cable connections.
Looks mean little.
Disconnect both of the battery cable lugs from the battery, and clean them up till they're shiny. A battery brush if you don't have one is a cheap investment, and makes this job real easy. Avoid the reamer type ones if you are shopping for one. They only remove good material. You want the wire brush kind. Check to make sure the cables don't have "green growth" (oxidized copper) around the battery lugs. This would indicate that the current, or a previous battery was leaking acid which wicked up the cables, and damaged them. If you find green growth, replace the cables. Next.. Take the battery cables off the motor, solenoid, and starter, and clean both ends of the connections with a wire brush till they are spotless. Re-attach, making sure the bolts/nuts are nice and snug. May want to spray them with a little of your favorite rattle can paint, or dab a little bit of dielectric grease on them. Anything to protect them from future corrosion.
Try starting the motor again.
Is it working? Open up a frosty adult beverage to celebrate, or even a soda/pop/coke if adult beverages aren't your thing.
Not so much? Well at least everything that could be questioned as causing the problem 90% of the time has been looked over, now it's time to check out the starter.