Probably the battery, alternator or starter, in that order. I would suspect it's the battery or alternator since you were able to push start it. If your battery is over 3-4 yrs old, I would replace a new one from Costco (cheap and good) or get an Interstate (the best). Also check for rust around the battery cable/terminal.

 

I see this problem every day at work its most likely to be the starter the easy way to tell is crank the engine over when u get the clicking noise get something to hit the starter with, like a hammer give a few hard hits and crank it over, it should start, if t his is the case the starter motor will most likely to be out of brushes. u should get the battery tested, not many batterys crap out in the frist year.

 

Sounds like the starter solenoid to me...my car does it all the time...its takes 2-3 turns of the key to get my engine to start cranking, otherwise I just get a click...I'm used to it, doesn't bother me anymore..

 

Download the Factory Manual at http://www.iluvmyrx7.com It has all you need to find where different componets are and the testing and removal. Yeah. Starter solenoid.