could the ignition cylinder be the reason my car wont start

What is your question?

its a 2000 saturn SL2 and well I bought it with ignition problems because the key was hard to turn over so I started leaving the key on and the key would come out and then my battery started to die so I had to get jumps and then all of a sudden I was getting a jump and it wouldn't start anymore I put a new battery and still don't start