when you say you hear the starter clicking and whining, does that mean the engine is turning over? Starters when they go bad, generally will make a whirring noise but you won't hear the actual turning over noise you're used to hearing. That's because the starter is not engaging the flywheel. So if it is just whirring, then it is your starter, otherwise, it is something else.

BTW, if it is a bad starter, take a hammer and whack on the starter housing a few times beforehand, that will force the starter to engage the flywheel and allow you to start the car. It's not a permanent fix, but will get you out of a bind until you get a new starter.