No starting, after new battery and new alternator?

My car lights are all on, checked all the fuses, replaced battery and alternator, but when I go to start the engine, it turns over and then stops, sometimes the starter will spin by itself when trying to start it. Like it won't engage to the flywheel. No clicking, I don't consider the noise it makes when I try to start it as a click, it's like it tries to turn over the engine almost doesn't like the engine is seized! I gave someone a jump start, then after they took off, I started to lose power and it shut off and wouldn't start. Now when it shut off before and the security was engaged it wouldn't do anything when I turn the key.