1997 Toyota Corolla starter

Electrical problem
1997 Toyota Corolla Automatic 121441 miles

I got into my vehicle and turn the key but it wouldnt start. Everything in the car that runs on the battery comes on with out problems. When you turn the key the sound the car makes is something similar to when you place something in the spokes of a bicycle I was wondering if that was the starter gone bad or alternator or something else pricey.I appriciate your help in advanced