1990 Camaro RS 5.0L V8 TBI OHV 16V / REAR WHEEL DRIVE

I recently purchaed a camaro but it wont start on its own. When I bought u I saw it had a new alternator and the battery seemed bad and not the right battery for a v8, so I thoguht that was the reason why the car needed to be jumped in order for it to start. So I bought a new battery put it in there and still did not start. Jumped it and the car started. So then I had the starter checked out and its fine. Somethign seems to be draining the new battery. I just do not know what is wrong with it. It has 120000 and I beleive the engine is a 305. It had an alarm and the wire is cut so it doesnt go off the security light would turn on in the dash board but when I was able to start the car by jumping it I figured the battery had nothing to do with it. :( Oh I could also hear a small clikcing sound when turning the key so thats why at first I tought somethign was stopping the car from turning on b/c all the lights turn even the air in the engine but not the engine itself. When I was able to drive it the rpm wa very high I only went about 70mph b/c I didnt want to hit the red section of the rpm. But I just want to turn the car on by itself wihtout umping it at this point.