Fuel Problem 2000 Cavalier

Here is the situation. Car was driving on the highway, suddenly when I stepped on the gas nothing happened, pulled the car over and it stayed Idling but wouldnt rev past 3000rpms.

Had the car towed and when I got it home it wouldnt turn over so I suspected it was the ant-theft. I charged the battery back up and waited for awhile and tried starting the car.

The car sputtered and then finally fired right up and idled normal, but when I rev the engine it gets up to 3500rpms then sputters and drops back down to about 2000rpms and starts to climb again, when it reaches 3500 rpms it does the same thing. Back and forth over and over.

So, I'm thinking it's starved for fuel... What do you think? Fuel pump? Fuel filter? Injectors dirty? What would cause the car to only sputter when it gets to 3500 rps and themn drop back down?

ANY ideas on how to go about fixing this would be GREAT because I'm not sure where to go from here.

Well odds are the injectors wouldn't cause this because you would probably only notice it in one maybe two cylinders to this degree. For how cheap fuel filters cost i would say that wouldn't hurt (not to mention you probably need it changed anyway) but to me it sounds like its hitting a limit and getting kicked back. Does the car sputter rough or does it just kick back to 2000ish and climb again?