hey jb...
A bad battery (fully drained) will not have enough juice to turn over the starter. The clicking noise is typical when it is in this state. I doubt that your starter is affected. Corroded terminals are a sign of drainage usually from a small drain like a dome light left on or a radio/electrical connection touching ground when the vehicle is off. After a few days, the battery becomes drained to the point that it struggles to turn over and eventually not start.
I've noticed that the stock original battery does not last more than 2 years max and it may be that time for you to get a new replacement. Even if you had the battery jumped to start the engine, it will eventually drain out and won't crank on your next start attempt.. When a battery gets to this level, it may not take a charge again and becomes unsalvageable.
There are places like Kragen Auto who will credit you $10 or $20 towards the purchase of a new battery when you trade in your old one. You also may want to consider other batteries like the yellow or red top (depending on your needs) Optima batteries. Several members here have them and swear by them. Hope this helps.
For custom VehiCross skidplates and accessories, check out:
www.aftershockproducts.com