Big Sonata Trouble!!!

Hello!  My 2001 Sonata which is a 4 cylinder; 2.0 (not sure on the liters) has given me soooo much trouble since I bought it.  I bought it with approximately 47,500 miles on it.  It was previously a rental, however alot of major stuff has been serviced on it.  More recently, at startup, the car runs very roughly then idles down after a few minutes.  When I begin to give it gas, the car is sluggish and sort of like "bucks" like it wants to cut off.  In addition makes a grinding noise at high RPMS.  As of yesterday, I started the car to hear the grinding noise again.  Attempting to replicate the noise a again, I turned the car back off only to find it will not turn over at all.  I do however, have power to all electronic stuff (windows, radio, lights, sunroof, etc....)  It appears the battery is working just fine.  Could it be the starter?